Question 11 Mark
Using properties of sets, show that: $A \cap (A \cup B) = A$
AnswerWe know that if $A \subset B$ then
$A \cap B = A$
Also $A \subset A \cup B$
$\therefore A \cap (A \cup B) = A$
View full question & answer→Question 21 Mark
Using properties of set, show that: $A \cup (A \cap B) = A$
AnswerWe know that if $A \subset B$ then
$A \cap B = B$
Also $A \cap B \subset A$
$\therefore A \cup (A \cap B) = A$
View full question & answer→Question 31 Mark
Show that if $A \subset B$ then $C - B \subset C - A.$
AnswerLet $x \in C - B \Rightarrow x \in C$ and $x \notin B$
$\Rightarrow x \in C$ and $x \notin A$ $[\because A \subset B]$
$\Rightarrow x \in C - A$ Hence $C - B \subset C - A.$
View full question & answer→Question 41 Mark
Show that $A \cap B = A \cap C$ need not imply B = C.
AnswerLet A = {1, 2, 3, 4} , B = {2, 3, 4, 5, 6}, C = {2, 3, 4, 9, 10}
$\therefore A \cap B$= {1, 2, 3, 4} $ \cap $ {2, 3, 4, 5, 6}
= {2,3, 4}
$A \cap C$= {1, 2, 3, 4}, B = {2, 3, 4, 5, 6}, C = {2, 3, 4, 9, 10}
= {2, 3, 4}
$A \cap C$= {1, 2, 3, 4} $ \cap $ {2, 3, 4, 9, 10}
= {2, 3, 4}
Now we have $A \cap B = A \cap C$
But $B \ne C$
View full question & answer→Question 51 Mark
Let U be the set of all triangles in a plane. If A is the set of all triangles with at least one angle different from 60° what is ${A'}$?
AnswerHere U = {x : x is a triangle}
A = {x : x is a triangle and has at least one angle different from 60°}
$\therefore A' = U - A = ${x : x is a triangle} - {x : x is a triangle and has atleast one angle different from 60°}
= {x : x is a triangle and has all angles equal to 60°}
= Set of all equilateral triangles.
View full question & answer→Question 61 Mark
Draw appropriate Venn diagram for: A' $\cup$ B'
AnswerThe Venn diagram for A' $\cup$ B' The shaded portion represents A' $\cup$ B'
View full question & answer→Question 71 Mark
Draw appropriate Venn diagram for: $(A \cap B)'$
AnswerThe Venn diagram for $(A \cap B)'$The shaded portion represents $(A \cap B)'$
View full question & answer→Question 81 Mark
Draw appropriate Venn diagram for: A' $\cap$ B'
AnswerThe Venn diagram for A' $\cap$ B' The shaded portion represents A' $\cap$ B'
View full question & answer→Question 91 Mark
Draw appropriate Venn diagram for: $(A \cup B)'$
AnswerThe Venn diagram for $(A \cup B)'$The shaded portion represents $(A \cup B)'$
View full question & answer→Question 101 Mark
Taking the set of natural numbers as the universal set, write down the complement of the set: {x : 2x + 5 = 9}
AnswerHere $U = \{ x:x \in N\}$
Let A = {x : 2x + 5 = 9{ = {2}
$A' = U - A = \{ x:x \in N\} - \{ 2\}$
$= \{ x:x \in N,x \ne 2\}$
View full question & answer→Question 111 Mark
Taking the set of natural numbers as the universal set, write down the complement of the set: {x : x + 5 = 8}
AnswerHere $U = \{ x:x \in N\}$
Let A = {x : x + 5 = 8} = {3}
$A' = U - A = \{ x:x \in N\} -$
$= \{ x:x \in N,x \ne 3\}$
View full question & answer→Question 121 Mark
Taking the set of natural numbesrs as the universal set, write down the complement of the set: {x : x is a perfect cube}
AnswerHere $U = \{ x:x \in N\}$
Let A = {x : x is a perfect cube}
$A' = U - A = \{ x:x \in N\} -${x : x is a perfect cube}
= {x : x $ \in $N , x is not a perfect cube}
View full question & answer→Question 131 Mark
Taking the set of natural numbers as the universal set, write down the complement of the set: {x : x is a perfect square}
AnswerHere $U = \{ x:x \in N\}$
Let A = {x : x is a perfect square}
$A' = U - A = \{ x:x \in N\} -$ {x : x is a perfect square}
= { $x:x \in N$, x is not a perfect square}
View full question & answer→Question 141 Mark
Taking the set of natural numbers as the universal set, write down the complement of the set: {x : x is a natural number divisible by 3 and 5}
AnswerHere $U = \{ x:x \in N\}$
Let A = {x : x is a natural number divisible by 3 and 5}
$A' = U - A = \{ x:x \in N\} -$ {x : x is a natural number divisible by 3 and 5}
= {$x:x \in N$} - {x : x is a natural number divisible by 15}
= { $x:x \in N$, x is not divisible by 15}
View full question & answer→Question 151 Mark
Taking the set of natural numbers as the universal set, write down the complement of the set: {x : x is a prime number}
AnswerHere $U = \{ x:x \in N\}$
Let A = {x : x is a prime number}
$A' = U - A = \{ x:x \in N\} -${x : x is a prime number}
= { $x:x \in N$, x is not a prime number}
or {x : x is positive composite number and x = 1}
View full question & answer→Question 161 Mark
Taking the set of natural numbers as the universal set, write down the complement of the set: {x : x is a positive multiple of 3}
AnswerHere $U = \{ x:x \in N\}$
Let A = {x : x is a positive multiple of 3}
$\therefore A' = U - A = \{ x:x \in N\} -${x :x is a positive multiple of 3}
= { $x:x \in N$, x is not a multiple of 3}
View full question & answer→Question 171 Mark
Taking the set of natural numbers as the universal set, write down the complement of the set: {x : x is an odd natural number}
AnswerHere $U = \{ x:x \in N\}$ Let A = {x : x is an odd natural number}
$A' = U - A = \{ x:x \in N\} -${x : x is an odd natural number}
= {x : x is an even natural number}
View full question & answer→Question 181 Mark
Taking the set of natural numbers as the universal set, write down the complement of the set: $\{ x:x \in N\,\,and\,\,2x + 1 > 10\}$
AnswerHere $U = \{ x:x \in N\}$
Let A = {$x:x \in N$ and 2x + 1 > 10} = {5, 6, 7, 8 , . . . }
$A' = U - A = \{ x:x \in N\} - \{ 5,6,7,8,.....\}$
= {1, 2, 3, 4}
View full question & answer→Question 191 Mark
Taking the set of natural numbers as the universal set, write down the complement of the set: $\{ x:x \ge 7\}$
AnswerHere $U = \{ x:x \in N\}$
Let $A = \{ x:x \geqslant 7\} = \{ 7,8,9,10,......\}$
$A' = U - A = \{ x:x \in N\} - \{ 7,8,9,10,.....\}$
= {1, 2, 3, 4, 5, 6}
= {$x:x \in N$ and x < 7}
View full question & answer→Question 201 Mark
Taking the set of natural numbers as the universal set, write down the complement of the set: {x : x is an even natural number}
AnswerHere $U = \{ x:x \in N\}$
Let A = {x : x is an even natural number}
$A' = U - A = \{ x:x \in N\} -${x : x is an even natural number}
= {x : x is an odd natural number}
View full question & answer→Question 211 Mark
If U = {a, b, c, d, e, f, g, h}, find the complement of the set: D = {f, g, h, a}
Answer $D' = U - D = \{ a,b,c,d,e,f,g,h\} - \{ f,g,h,a\}$={b, c, d, e}
View full question & answer→Question 221 Mark
If U = {a, b, c, d, e, f, g, h}, find the complement of the set: C = {a, c, e, g}
Answer $C' = U - C = \{ a,b,c,d,e,f,g,h\} - \{ a,c,e,g\}$= {b, d, f, h}
View full question & answer→Question 231 Mark
If U = {a, b, c, d, e, f, g, h}, find the complement of the set: B = {d, e, f, g}
Answer $B' = U - B = \{ a,b,c,d,e,f,g,h\} - \{ d,e,f,g\}$={a, b, c, h}
View full question & answer→Question 241 Mark
If U = {a, b, c, d, e, f, g, h}, find the complement of the set: A = {a, b, c}
Answer $A' = U - A = \{ a,b,c,d,e,f,g,h\} - \{ a,b,c\}$= {d, e, f, g, h}
View full question & answer→Question 251 Mark
Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, B = {2,4, 6, 8} and C = {3, 4, 5, 6}. Find: (B - C)'
AnswerHere U = {1, 2, 3, 4, 5, 6, 7, 8, 9},
B - C = {2, 4, 6, 8} - {3, 4, 5, 6}
= {2, 8}
(B - C)' = U - (B - C) = {1, 2, 3, 4, 5, 6, 7, 8, 9} - {2, 8}
= {1, 3, 4, 5, 6, 7, 9}
View full question & answer→Question 261 Mark
Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, B = {2, 4, 6, 8} and C = {3, 4, 5, 6}. Find: (A')'
AnswerHere U = {1, 2, 3, 4, 5, 6, 7, 8, 9},
A' = U - A' = {1, 2, 3, 4, 5, 6, 7, 8, 9} - {5, 6, 7, 8, 9}
= {5, 6, 7, 8, 9}
A' = U - A' = {1, 2, 3, 4, 5, 6, 7, 8, 9} - {5, 6, 7, 8, 9}
= {1, 2, 3, 4} = A
View full question & answer→Question 271 Mark
Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, B = {2,4, 6, 8} and C = {3, 4, 5, 6}. Find: $(A \cup B)'$
AnswerHere U = {1, 2, 3, 4, 5, 6, 7, 8, 9},
$A \cup B $ = {1, 2, 3, 4} $ \cup $ {2, 4, 6 ,8}
= {1, 2, 3, 4, 6, 8}
$(A \cup B)' = U - (A \cup B)$ = {1, 2, 3, 4, 5, 6, 7, 8, 9} - {1, 2, 3, 4, 6, 8}
= {5, 7, 9}
View full question & answer→Question 281 Mark
Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, B = {2,4, 6, 8} and C = {3, 4, 5, 6}.
Find: $(A \cup C)'$
AnswerHere U = {1, 2, 3, 4, 5, 6, 7, 8, 9},
$A \cup C$ = {1, 2, 3, 4} $ \cap $ {3, 4, 5, 6}
= {1, 2, 3, 4, 5, 6}
$(A \cup C)' = U - (A \cup C)$= {1, 2, 3, 4, 5, 6, 7, 8, 9} - {1, 2, 3, 4, 5, 6}
={7, 8, 9}
View full question & answer→Question 291 Mark
Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, B = {2,4, 6, 8} and C = {3, 4, 5, 6}. Find: B'
AnswerHere U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, B = {2, 4, 6, 8} and C = {3, 4, 5, 6}
B' = U - B = {1, 2, 3, 4, 5, 6, 7, 8, 9} - {2, 4, 6, 8}
= {1, 3, 5, 7, 9}
View full question & answer→Question 301 Mark
Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {1, 2, 3, 4}, B = {2,4, 6, 8} and C = {3, 4, 5, 6}. Find : $\begin{equation} \mathbf{A}^{\prime} \end{equation}$
Answerwe have to find the complement of, which is given by (U - A)
Where U = {1, 2, 3, 4, 5, 6, 7, 8, 9} and A = {1, 2, 3, 4},
$\therefore$ $\begin{equation} \mathbf{A}^{\prime} \end{equation}$ = U - A
$\Rightarrow$ $\begin{equation} \mathbf{A}^{\prime} \end{equation}$ = {1, 2, 3, 4, 5, 6, 7, 8, 9} - {1, 2, 3, 4}
$\Rightarrow$ $\begin{equation} \mathbf{A}^{\prime} \end{equation}$ ={5, 6, 7, 8, 9}
View full question & answer→Question 311 Mark
If A = {3, 6, 9, 12, 15, 18, 21}, B = {4, 8, 12,16, 20}, C = {2, 4, 6, 8, 10, 12, 14, 16}, D = {5, 10, 15, 20}, find: C - B
AnswerHere A = {3, 6,9, 12, 15, 18, 21}, B = {4, 8, 12, 16, 20}, C = {2, 4, 6, 8, 10, 12, 14, 16}, D = {5, 10, 15, 20}
C - B = {2,4,6,8,10,12,14,16} - {4,8,12,16,20}
= {2,6,10,14}
View full question & answer→Question 321 Mark
If A = {3, 6, 9, 12, 15, 18, 21}, B = {4, 8, 12, 16, 20}, C = {2, 4, 6, 8, 10, 12, 14, 16}, D = {5, 10, 15, 20}. Find: B - D.
AnswerHere A = {3, 6, 9, 12, 15, 18, 21}, B = {4, 8, 12, 16, 20}, C = {2, 4, 6, 8, 10, 12, 14, 16}, D = {5, 10, 15, 20}
B - D = {4, 8, 12, 16, 20} - {5, 10, 15, 20}
= {4, 8, 12, 16}
View full question & answer→Question 331 Mark
If A = {3, 6, 9, 12, 15, 18, 21}, B = {4, 8, 12,16, 20}, C = {2, 4, 6, 8, 10, 12, 14, 16}, D = {5, 10, 15, 20}. Find: B - C
AnswerHere A = {3, 6, 9, 12, 15, 18, 21}, B = {4, 8, 12, 16, 20}
C = {2, 4, 6, 8, 10, 12, 14, 16}, D = {5, 10, 15, 20}
B - C = {4, 8, 12, 16, 20} - {2, 4, 6, 8, 10, 12, 14, 16}
= {20}
View full question & answer→Question 341 Mark
If A = {3, 6, 9, 12, 15, 18, 21}, B = {4, 8, 12,16, 20}, C = {2, 4, 6, 8, 10, 12, 14, 16}, D = {5, 10, 15, 20}. Find: D - A
AnswerHere A = {3, 6, 9, 12, 15, 18, 21}, B = {4, 8, 12, 16, 20}, C = {2, 4, 6, 8, 10, 12, 14, 16}, D = {5, 10, 15, 20}
D - A = {5, 10, 15, 20} - {3, 6, 9, 12, 15, 18, 21}
= {5, 10, 20}
View full question & answer→Question 351 Mark
If A = {3, 6, 9, 12, 15, 18, 21}, B = {4, 8, 12,16, 20}, C = {2, 4, 6, 8, 10, 12, 14, 16}, D = {5, 10, 15, 20}, find: C - A
AnswerHere A = {3, 6,9, 12, 15, 18, 21}, B = {4, 8, 12, 16, 20}, C = {2, 4, 6, 8, 10, 12, 14, 16}, D = {5, 10, 15, 20}
C - A = {2,4,6,8,10,12,14,16} - {3,6,9,12,15,18,21}
= {2,4,8,10,14,16}
View full question & answer→Question 361 Mark
If A = {3, 6, 9, 12, 15, 18, 21}, B = {4, 8, 12,16, 20}, C = {2, 4, 6, 8, 10, 12, 14, 16}, D = {5, 10, 15, 20}, find: B - A
AnswerHere A = {3, 6, 9, 12, 15, 18, 21}, B = {4, 8, 12, 16, 20}, C = {2, 4, 6, 8, 10, 12, 14, 16}, D = {5, 10, 15, 20}
B - A = {4, 8, 12, 16, 20} - {3, 6, 9, 12, 15, 18, 21}
= {4, 8, 16, 20}
View full question & answer→Question 371 Mark
If A = {3, 6, 9, 12, 15, 18, 21}, B = {4, 8, 12,16, 20}, C = {2, 4, 6, 8, 10, 12, 14, 16}, D = {5, 10, 15, 20}, find: A - D
AnswerHere A = {3, 6, 9, 12, 15, 18, 21}, B = {4, 8, 12, 16, 20}, C = {2, 4, 6, 8, 10, 12, 14, 16}, D = {5, 10, 15, 20}
A - D = {3, 6, 9, 12, 15, 18, 21} - {5, 10, 15, 20}
= {3, 6, 9, 12, 18, 21}
View full question & answer→Question 381 Mark
If A = {3, 6, 9, 12, 15, 18, 21}, B = {4, 8, 12,16, 20}, C = {2, 4, 6, 8, 10, 12, 14, 16}, D = {5, 10, 15, 20}, find: A - C
AnswerHere A = {3, 6, 9, 12, 15, 18, 21}, B = {4, 8, 12, 16, 20}
C = {2, 4, 6, 8, 10, 12, 14, 16}, D = {5, 10, 15, 20}
A - C = {3, 6, 9, 12, 15, 18, 21} - {2, 4, 6, 8, 10, 12, 14, 16}
={3, 9, 15, 18, 21}
View full question & answer→Question 391 Mark
If A = {3, 6, 9, 12, 15, 18, 21}, B = {4, 8, 12,16, 20}, C = {2, 4, 6, 8, 10, 12, 14, 16}, D = {5, 10, 15, 20}, find: D - C
AnswerHere A = {3, 6,9, 12, 15, 18, 21}, B = {4, 8, 12, 16, 20}, C = {2, 4, 6, 8, 10, 12, 14, 16}, D = {5, 10, 15, 20}
D - C = {5,10,15,20} - {2,4,6,8,10,12,14,16}
= {5,15,20}
View full question & answer→Question 401 Mark
If A = {3, 6, 9, 12, 15, 18, 21}, B = {4, 8, 12,16, 20}, C = {2, 4, 6, 8, 10, 12, 14, 16}, D = {5, 10, 15, 20}, find: C - D
AnswerHere A = {3, 6,9, 12, 15, 18, 21}, B = {4, 8, 12, 16, 20}, C = {2, 4, 6, 8, 10, 12, 14, 16}, D = {5, 10, 15, 20}
C - D = {2,4,6,8,10,12,14,16} - {5,10,15,20}
= {2,4,6,8,12,14,16}
View full question & answer→Question 411 Mark
If A = {3, 6, 9, 12, 15, 18, 21}, B = {4, 8, 12,16, 20}, C = {2, 4, 6, 8, 10, 12, 14, 16}, D = {5, 10, 15, 20}, find: D - B
AnswerHere A = {3, 6,9, 12, 15, 18, 21}, B = {4, 8, 12, 16, 20}
C = {2, 4, 6, 8, 10, 12, 14, 16}, D = {5, 10, 15, 20}
D - B = {5,10,15,20} - {4,8,12,16,20}
= {5,10,15}
View full question & answer→Question 421 Mark
If A = {3, 6, 9, 12, 15, 18, 21}, B = {4, 8, 12,16, 20}, C = {2, 4, 6, 8, 10, 12, 14, 16}, D = {5, 10, 15, 20}, find: A - B
AnswerHere A = {3, 6, 9, 12, 15, 18, 21}, B = {4, 8, 12, 16, 20}
C = {2, 4, 6, 8, 10, 12, 14, 16}, D = {5, 10, 15, 20}
A - B = {3, 6, 9, 12, 15, 18, 21} - {4, 8, 12, 16, 20}
= { 3, 6, 9, 15, 18, 21}
View full question & answer→Question 431 Mark
Given pair of sets are disjoint? {x : x is an even integer} and {x : x is an odd integer}
AnswerLet A = {x : x is an even integer}
and B = {x : x is an odd integer}
$\therefore A \cap B = \phi $
Hence A and B are disjoint.
View full question & answer→Question 441 Mark
Given pair of sets are disjoint? {a, e, i, o, u} and {c, d, e, f}
Answer(ii) Let A = {a, e, i, o, u}
and B = {c, d, e, f}
$\therefore A \cap B ≠ \phi$
Hence A and B are not disjoint.
View full question & answer→Question 451 Mark
Given pair of sets are disjoint? {1, 2, 3, 4} and {x : x is a natural number and $4 \leq x \leq 6$
AnswerLet A = {1, 2, 3, 4}
and B = {x : x is a natural number and $4 \leq x \leq 6$
= {4, 5, 6}
$\therefore A \cap B = \{ 1,2,3,4\} \cap \{ 4,5,6\}$
= {4}
Hence A and B are not disjoint.
View full question & answer→Question 461 Mark
If A = {x : x is a natural number}, B = {x : x is an even natural number}, C = {x : x is an odd natural number} and D = {x : x is a prime number}, find: $C \cap D$
AnswerHere A = {x : x is a natural number} = {1, 2, 3, 4, 5, . . .}
B = { x : x is an even natural number} = {2, 4, 6, . . . }
C = {x : x is an odd natural number} = {1, 3, 5, 7, . . .}
and D = {x : x is a prime nmber} = {2, 3, 5, 7. . . . } $C \cap D$ = {x : x is an odd natural number} $ \cap ${x : x is a prime number}
= {x : x is an odd prime number}
View full question & answer→Question 471 Mark
If A = {x : x is a natural number}, B = {x : x is an even natural number}, C = {x : x is an odd natural number} and D = {x : x is a prime number}, find: $B \cap D$
AnswerHere A = {x : x is a natural number} = {1, 2, 3, 4, 5, . . .}
B = { x : x is an even natural number} = {2, 4, 6, . . . }
C = {x : x is an odd natural number} = {1, 3, 5, 7, . . .}
and D = {x : x is a prime nmber} = {2, 3, 5, 7. . . . } $B \cap D$ = {x : x is an even natural number) $ \cap ${x : x is a prime number}
= {2}
View full question & answer→Question 481 Mark
If A = {x : x is a natural number}, B = {x : x is an even natural number}, C = {x : x is an odd natural number} and D = {x : x is a prime number}, find: $B \cap C$
AnswerHere A = {x : x is a natural number} = {1, 2, 3, 4, 5, . . .}
B = { x : x is an even natural number} = {2, 4, 6, . . . }
C = {x : x is an odd natural number} = {1, 3, 5, 7, . . .}
and D = {x : x is a prime nmber} = {2, 3, 5, 7. . . . } $B \cap C$= {x : x is an even natural number} $ \cap${x : x is an odd natural number}
$ = \phi $
View full question & answer→Question 491 Mark
If A = {x : x is a natural number}, B = {x : x is an even natural number}, C = {x : x is an odd natural number} and D = {x : x is a prime number}, find: $A \cap D$
AnswerHere A = {x : x is a natural number} = {1, 2, 3, 4, 5, . . .}
B = { x : x is an even natural number} = {2, 4, 6, . . . }
C = {x : x is an odd natural number} = {1, 3, 5, 7, . . .}
and D = {x : x is a prime nmber} = {2, 3, 5, 7. . . . } $A \cap D$= {x : x is a natural number) $ \cap${x : x is a prime number}
= {x : x is a prime number}
= D
View full question & answer→Question 501 Mark
If A = {x : x is a natural number}, B = {x : x is an even natural number}, C = {x : x is an odd natural number} and D = {x : x is a prime number}, find: $A \cap C$
AnswerHere A = {x : x is a natural number} = {1, 2, 3, 4, 5, . . .}
B = { x : x is an even natural number} = {2, 4, 6, . . . }
C = {x : x is an odd natural number} = {1, 3, 5, 7, . . .}
and D = {x : x is a prime nmber} = {2, 3, 5, 7. . . . } $A \cap C$ = {x : x is a natural number} $ \cap ${x : x is an odd natural number}
= { x : x is an odd natural number }
= C
View full question & answer→Question 511 Mark
If A = {x : x is a natural number}, B = {x : x is an even natural number}, C = {x : x is an odd natural number} and D = {x : x is a prime number}, find: $A \cap B$ ?
AnswerHere A = {x : x is a natural number} = {1, 2, 3, 4, 5, . . .}
B = { x : x is an even natural number} = {2, 4, 6, . . . }
C = {x : x is an odd natural number} = {1, 3, 5, 7, . . .}
and D = {x : x is a prime nmber} = {2, 3, 5, 7. . . . } $A \cap B$ = {x :x is a natural number)$ \cap $ {x : x is an even natural number}
= {x : x is an even natural number}
= B
View full question & answer→Question 521 Mark
If A = {3, 5, 7, 9, 11} , B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17} find: $(A \cap B) \cap (B \cup C)$
AnswerHere A = {3, 5, 7, 9, 11} , B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17} $(A \cap B) \cap (B \cup C) =$$(\{ 3,5,7,9,11\} \cap \{ 7,9,11,13\} ) \cap (\{ 7,9,11,13\} \cup \{ 11,13,15\} )$
$ = \{ 7,9,11\} \cap \{ 7,9,11,13,15\}$
= {7, 9, 11}
View full question & answer→Question 531 Mark
If A = {3, 5, 7, 9, 11} , B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17} find: $A \cap (B \cup D)$
AnswerHere A = {3,5,7,9,11}, B = {7,9,11,13}, C = {11,13,15} and D = {15,17} $A \cap (B \cup D) = $$A \cap (B \cup D) = \{ 3,5,7,9,11\} \cap (\{ 7,9,11,13\} \cup \{ 15,17\} )$
$ = \{ 3,5,7,9,11\} \cap \{ 7,9,11,13,15,17\} $
= {7,9, 11}
View full question & answer→Question 541 Mark
If A = {3, 5, 7, 9, 11} , B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17} find $A \cap D$
AnswerHere A = {3, 5, 7, 9, 11} , B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17} $A \cap D = \{ 3,5,7,9,11\} \cap \{ 15,17\} = \phi $
View full question & answer→Question 551 Mark
If A = {3, 5, 7, 9, 11} , B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17} find: $A \cap (B \cup C)$
AnswerHere A = {3,5,7,9,11}, B = {7,9,11,13}, C = {11,13,15} and D = {15,17} $A \cap (B \cup D) = \{ 3,5,7,9,11\} \cap (\{ 7,9,11,13\} \cup \{ 11,13,15\} )$
$ = \{ 3,5,7,9,11\} \cap \{ 7,9,11,13,15\} $
= {7, 9, 11}
View full question & answer→Question 561 Mark
If A = {3, 5, 7, 9, 11} , B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17} find: $B \cap D$
AnswerHere A = {3,5,7,9,11}, B = {7,9,11,13}, C = {11,13,15} and D = {15,17} $B \cap D = \{ 7,9,11,13\} \cap \{ 15,17\} = \phi $
View full question & answer→Question 571 Mark
If A = {3, 5, 7, 9, 11} , B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17} find $A \cap C$
AnswerHere A = {3, 5, 7, 9, 11} , B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17} $A \cap C = \{ 3,5,7,9,11\} \cap \{ 11,13,15\}$= {11}
View full question & answer→Question 581 Mark
If A = {3, 5, 7, 9, 11} , B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17} find $A \cap C \cap D$
AnswerHere A = {3, 5, 7, 9, 11} , B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17} $A \cap C \cap D = \{ 3,5,7,9,11\} \cap \{ 11,13,15\} \cap \{ 15,17\} = \phi $
View full question & answer→Question 591 Mark
If A = {3, 5, 7, 9, 11} , B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17} find $B \cap C$
AnswerHere A = {3, 5, 7, 9, 11} , B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17} $B \cap C = \{ 7,9,11,13\} \cap \{ 11,13,15\} $= {11, 13}
View full question & answer→Question 601 Mark
If A = {3, 5, 7, 9, 11} , B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17} find:$(A \cup D) \cap (B \cup C)$
AnswerHere A = {3, 5, 7, 9, 11} , B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17} $(A \cup D) \cap (B \cup C) = $$(\{ 3,5,7,9,11\} \cup \{ 15,17\} ) \cap (\{ 7,9,11,13\} \cup \{ 11,13,15\} )$
$ = \{ 3,5,7,9,11,13,15,17\} \cap \{ 7,9,11,13,15\}$
= {7, 9, 11,15}
View full question & answer→Question 611 Mark
If A = {3, 5, 7, 9, 11} , B = {7, 9, 11, 13}, C = {11, 13, 15} and D = {15, 17} find: $A \cap B$?
AnswerHere A = {3,5,7,9,11}, B = {7,9,11,13}, C = {11,13,15} and D = {15,17} $A \cap B = \{ 3,5,6,7,11\} \cap \{ 7,9,11,13\} = \{ 7,9,11\}$
View full question & answer→Question 621 Mark
Find the intersection pair of the set : A = {1, 2, 3}, B = $\phi$
AnswerWe have,
A = {1, 2, 3}
And, B = $\phi$
$\therefore$ A $\cap$ B = {$\phi$}
View full question & answer→Question 631 Mark
Find the intersection pair of the set : A = {x : x is a natural number and 1 < x $\leq$ 6 }, B = {x : x is a natural number and 6 < x < 10}
AnswerWe have,
A = {2, 3, 4, 5, 6}
And, B = {7, 8, 9}
$\therefore$ A $\cap$ B = {$\phi$}
View full question & answer→Question 641 Mark
Find the intersection pair of the set : A = {x : x is a natural number and multiple of 3}, B = {x : x is a natural number less than 6}
AnswerGiven,
A = {3, 6, 9, 12, 15, 18, ....}
And, B = {1, 2, 3, 4, 5}
$\therefore$A $\cap$ B = {a}
View full question & answer→Question 651 Mark
Find the intersection pair of the set : A = {a, e, i, o, u} B = {a, b, c}
AnswerWe have
A = {a, e, i, o, u}
And, B = {a, b, c}
$\therefore$ A $\cap$ B = {a}
View full question & answer→Question 661 Mark
Find the intersection pair of the set : X = {1, 3, 5} Y = {1, 2, 3}
AnswerHere, we have
X = {1, 3, 5}
And, Y = {1, 2, 3}
$\therefore$ X $\cap$ Y = {1, 3}
View full question & answer→Question 671 Mark
If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8} and D = {7, 8, 9, 10} find: $B \cup C \cup D$
AnswerHere A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8} and D ={7, 8, 9, 10} $B \cup C \cup D =$
$= \{ 3,4,5,6\} \cup \{ 5,6,7,8\} \cup \{ 7,8,9,10\}$
$= \{ 3,4,5,6,7,8\} \cup \{ 7,8,9,10\}$
= {3, 4, 5, 6, 7, 8, 9,10}
View full question & answer→Question 681 Mark
If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8} and D = {7, 8, 9, 10} find: $A \cup B \cup D$
AnswerHere A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8} and D ={7, 8, 9, 10} $A \cup B \cup D = \{ 1,2,3,4\} \cup \{ 3,4,5,6\} \cup \{ 7,8,9,10\}$
$= \{ 1,2,3,4,5,6\} \cup \{ 5,6,7,8\}$
= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
View full question & answer→Question 691 Mark
If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8} and D = {7, 8, 9, 10} find: $A \cup B \cup C$
AnswerHere A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8} and D ={7, 8, 9, 10} $A \cup B \cup C = \{ 1,2,3,4\} \cup \{ 3,4,5,6\} \cup \{ 5,6,7,8\} $
$= \{ 1,2,3,4,5,6\} \cup \{ 5,6,7,8\}$
= {1, 2, 3,4, 5, 6, 7, 8}
View full question & answer→Question 701 Mark
If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8} and D = {7, 8, 9, 10} find: $B \cup D$
AnswerHere A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8} and D ={7, 8, 9, 10} $B \cup D = \{ 3,4,5,6\} \cup \{ 7,8,9,10\}$= {3, 4, 5, 6, 7, 8, 9, 10}
View full question & answer→Question 711 Mark
If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8} and D = {7, 8, 9, 10} find: $B \cup C$
AnswerHere A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8} and D ={7, 8, 9, 10} $B \cup C = \{ 3,4,5,6\} \cup \{ 5,6,7,8\}$= {3, 4, 5, 6, 7, 8}
View full question & answer→Question 721 Mark
If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8} and D = {7, 8, 9, 10} find: $A \cup C$
AnswerHere A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8} and D ={7, 8, 9, 10} $A \cup C = \{ 1,2,3,4\} \cup \{ 5,6,7,8\}$= {1, 2, 3, 4, 5, 6, 7, 8}
View full question & answer→Question 731 Mark
If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8} and D = {7, 8, 9, 10} find: $A \cup B$
AnswerHere A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8} and D ={7, 8, 9, 10} $A \cup B = \{ 1,2,3,4\} \cup \{ 3,4,5,6\}$= {1, 2, 3, 4, 5, 6}
View full question & answer→Question 741 Mark
If A and B are two sets such that $A \subset B,$ then what is $A \cup B$?
AnswerHere A and B are two sets such that $A \subset B$
Then $A \cup B$ = B
View full question & answer→Question 751 Mark
Let A = {a, b}, B = {a, b, c}. Is A $\subset$ B ? What is A $\cup$ B?
AnswerWe have,
$A =\{a, b\}$
And, B = {a, b, c}
Here, it is clearly seen that all the elements of set A are present in set B
$\therefore \ A \subset B$
And, $A \cup B=\{a, b, c\}=B$
View full question & answer→Question 761 Mark
Find the union pair of set: A = {1, 2, 3} and B = $\phi$
AnswerHere A = {1, 2, 3} and $B = \phi ,\,\,\therefore A \cup B = \{ 1,2,3\} $
View full question & answer→Question 771 Mark
Find the union pair of set: A = {x : x is a natural number and 1 < x $\leq$ 6} and B = {x : x is a natural number and 6 < x < 10}
AnswerHere A = {x : x is a natural number and $1 < x \leq 6$}
= {2, 3, 4, 5, 6}
and B = {x : x is a natural number and 6 < x < 10}
= {7, 8, 9}
$\therefore$ $A \cup B$ = {2,3,4,5,6,7,8,9}
View full question & answer→Question 781 Mark
Find the union pair of set: A = {x : x is a natural number and multiple of 3} and B = {x : x is a natural number less than 6}
AnswerHere A = {x : x is a natural number and multiple of 3}
= {3, 6, 9, 12, . . . }
and B = {x : x is a natural number less than 6}
= {1, 2, 3, 4, 5} $\therefore A \cup B = \{ 1,2,3,4,5,6,9,12,15,....\}$
View full question & answer→Question 791 Mark
{2, 6, 10} and {3, 7, 11} are disjoint sets.
Question 801 Mark
{2, 6, 10, 14} and {3, 7, 11, 15} are disjoint sets.
Question 811 Mark
{a, e, i, o, u) and {a, b, c, d} are disjoint sets.
Question 821 Mark
{2,3, 4, 5} and {3, 6} are disjoint sets.
Question 831 Mark
Find the union pair of set: A = {a, e, i, o, u} and B = {a, b, c}
AnswerHere A = {a, e, i, o, u} and B = {a, b, c}, $\therefore A \cup B = \{ a,b,c,e,i,o,u\}$
View full question & answer→Question 841 Mark
If R is the set of real numbers and Q is the set of rational numbers, then what is R - Q?
AnswerWe know that set of real numbers contain rational and irrational number.
So R - Q set of irrational numbers.
View full question & answer→Question 851 Mark
Find the union pair of set: X = {1, 3, 5} and Y = {1, 2, 3}
AnswerHere X = {1, 3, 5} and Y = {1, 2, 3}, $\therefore X \cup Y = \{ 1,2,3,5\}$
View full question & answer→Question 861 Mark
If X = {a, b, c, d} and Y = {f, b, d, g} find: $X \cap Y$
AnswerHere X = {a, b, c, d} and Y = {f, b, d, g} $X \cap Y = \{ a,b,c,d\} \cap \{ f,b,d,g\} $ = {b, d}
View full question & answer→Question 871 Mark
If X = {a, b, c, d} and Y = {f, b, d, g} find: Y - X
AnswerHere X = {a, b, c, d} and Y = {f, b, d, g}
Y - X = {f, b, d, g} - {a, b, c, d} = {f , g}
View full question & answer→Question 881 Mark
If X = {a, b, c, d} and Y = {f, b, d, g} find: X - Y
AnswerX - Y ={a, b, c, d} - {f, b, d, g}={a,c}
View full question & answer→Question 891 Mark
Given the set A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 6, 8}. Is {1, 2, 3, 4, 5, 6, 7, 8} be considered as universal set for all the three sets A, B and C?
Answer{1, 2, 3, 4, 5, 6, 7, 8} is not a universal set for A, B, C because $0 \in C$ but 0 is not a member of {1, 2, 3, 4, 5, 6,7, 8}.
View full question & answer→Question 901 Mark
Given the set A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 6, 8}. Is {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} be considered as universal set for all the three sets A, B and C?
Answer{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} is a universal set for A, B, C because all members of A, B, C are present in {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
View full question & answer→Question 911 Mark
Given the sets A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 6, 8}, Is $\phi$ be considered as universal set for all the three sets A, B and C?
AnswerGiven that- A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 6, 8}
Now, suppose D = $\phi$ Since,
D is an empty set ,it does not contain any element.
$Therefore $ D is not a universal set for A, B, C.
View full question & answer→Question 921 Mark
Given the set A = {1, 3, 5}, B = {2, 4, 6} and C = {0, 2, 4, 6, 8}. Is {0, 1, 2, 3, 4, 5, 6} be considered as universal set for all the three sets A, B and C?
Answer{{0,1, 2, 3, 4, 5, 6} is not a universal set for A, B, C, because $8 \in C$ but 8 is not a member of {0, , 2, 3, 4, 5, 6}
View full question & answer→Question 931 Mark
What universal set would you propose: The set of isosceles triangles.
AnswerIsosceles triangle is a type of triangle. So the set of triangles contain all types of triangles.
$\therefore$ U = {x : x is a triangle in plane}
View full question & answer→Question 941 Mark
What universal set would you propose: The set of right triangles.
AnswerRight triangle is a type of triangle. So the set of triangles contain all types of triangles.
$\therefore$ U = {x : x is a triangle in plane}
View full question & answer→Question 951 Mark
Write the interval [-23, 5) in set builder form.
AnswerThe interval [-23, 5) can be written in set builder form as $\{ x:x \in R, - 23 \leqslant x < 12\} $
View full question & answer→Question 961 Mark
Write the interval (6, 12] in set builder form.
AnswerThe interval (6, 12] can be written in set builder form as $\{ x:x \in R,6 \leqslant x \leqslant 12\}$
View full question & answer→Question 971 Mark
Write the interval [6, 12] in set builder form.
AnswerThe interval [6, 12] can be written in set builder form as $\{ x:x \in R,6 \leqslant x \leqslant 12\} $
View full question & answer→Question 981 Mark
Write the interval in set builder form (-3, 0)
AnswerThe interval (-3, 0) can be written in set builder form as $\{ x:x \in R, - 3 < x < 0\} $
View full question & answer→Question 991 Mark
Write $\{ X:X \in R,3 \leq X < 4\}$ as interval.
AnswerLet A = $\{ x \in R:3 \leq x \leq 4\}$
it can be written as [3,4]
View full question & answer→Question 1001 Mark
Write $\{ X:X \in R,0 \leq X < 7\}$ as interval.
AnswerLet A = $\{ x \in R:0 \leq x < 7\}$
it can be written as [0,7]
View full question & answer→Question 1011 Mark
Write $\{ X:X \in R, - 12 < X < - 10\}$ as interval.
AnswerLet A = $\{ X:X \in R, - 12 < X < - 10\}$ It can be written in the form of interval as [-12, -10]
View full question & answer→Question 1021 Mark
Write {x : x $\in$ R, -4 < x $\leq$ 6} as interval.
Answer{x : x $\in$ R, -4 < x $\leq$ 6} is the set that does not contain - 5 but contains 6.
So, it can be written as an interval whose first end-point is open and last end-point is closed i.e., (-4,6].
View full question & answer→Question 1031 Mark
How many elements has P(A), if $A = \phi $?
AnswerNumber of elements in set A = 0
Number of subsets of set A = 20 = 1
Hence number of element of P(A) is 1
View full question & answer→Question 1041 Mark
Write down the subsets of set : $\phi$
AnswerSuppose A = $\phi$
Now, number of elements in A = 0
Number of subsets of A = $2^0$ = 1
$\therefore$ subset of A is: $\phi$
View full question & answer→Question 1051 Mark
Write down the subsets of set : {1, 2, 3}
AnswerSuppose A= {1, 2, 3}
Now, number of elements in A = 3
Number of subsets of A = $2^3$ = 8
$\therefore$ subsets of A are given in below
ϕ, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3}, {1, 2, 3}
View full question & answer→Question 1061 Mark
Write down the subsets of set : {a, b}
AnswerSuppose A= {a, b}
Now, number of elements in A = 2
Number of subsets of A = $2^2$= 4
$\therefore$ subsets of A are: $\phi$, {a}, {b}, {a, b}
View full question & answer→Question 1071 Mark
Write down the subsets of set : {a}
AnswerSuppose A = {a}
Now, number of elements in A = 1
Number of subsets of A = $2^1$
$\therefore$ subsets of A are: $\phi$, {a}
View full question & answer→Question 1081 Mark
Let A = {1, 2, {3, 4 }, 5}. Is the statement $\phi \in$ A incorrect and why?
AnswerHere, we can see that $\phi$ is not a member of set A
Therefore, the given statement is correct.
View full question & answer→Question 1091 Mark
Let A = {1, 2, {3, 4 }, 5}. Is the statement {1, 2, 3} $\subset$ A incorrect and why?
AnswerHere, we can see that 3 is not a member of set A
= {1,2,3} is not a subset of A
Theyesore, the given statement is incorrect.
View full question & answer→Question 1101 Mark
Let A = {1, 2, {3, 4 }, 5}. Is the statement {1, 2, 5} $\in$ A incorrect and why?
AnswerHere, we can see that 1, 2, 5 is a member of set A
= {1, 2, 5} is a subset of A
Therefore, the given statement is incorrect.
View full question & answer→Question 1111 Mark
Let A = {1, 2, {3, 4}, 5}. Is the statement $\{ 1,2,5,\} \subset A$ incorrect and why?
Answer1, 2, 5, are members of set A.
$\therefore $ {1, 2, 5} is a subset of set A. $\therefore \{ 1,2,5\} \subset A$ is correct.
View full question & answer→Question 1121 Mark
Let A = {1, 2, {3, 4 }, 5}. Is the statement 1 $\subset$ A incorrect and why?
AnswerHere, we can see that 1 is a member of set A but is not any set itself.
Theyesore, the given statement is incorrect.
View full question & answer→Question 1131 Mark
Let A = {1, 2, {3, 4}, 5}. Is the statement $1 \in A$ incorrect and why?
Answer1 is a member of set A.
$\therefore 1 \in A$ is correct.
View full question & answer→Question 1141 Mark
Let A = {1, 2, {3, 4 }, 5}. Is the statement {{3, 4}} $\subset$ A is incorrect and why?
AnswerHere, we know that {3,4} is a member of set A = {{3,4}} is a set.
Therefore, the given statement is correct.
View full question & answer→Question 1151 Mark
Let A = {1, 2, {3, 4}, 5}. Is the statement {3, 4} $\in$ A incorrect and why?
Answer{3, 4} is a member of set A. $\therefore \{ 3,4\} \in A$ is correct.
View full question & answer→Question 1161 Mark
Let A = {1, 2, {3, 4 }, 5}. Is the statement {$\phi$} $\subset$ A incorrect and why?
Answer{$\phi$} is the set containing the null set.
$\{\phi\} \subset A$ is only possible if $\phi$ is in set A but it is not there. Therefore, the statement is incorrect.
View full question & answer→Question 1171 Mark
Let A = {1, 2, {3, 4}, 5}. Is the statement $\phi \subset A$ incorrect and why?
AnswerSince $\phi $ is subset of every set $\therefore \phi \subset A$ is correct
View full question & answer→Question 1181 Mark
Let A = {1, 2, {3, 4}, 5}. IIs the statement {3, 4} $\subset $ A incorrect and why?
Answer{3, 4} is a member of set A.
$\therefore \{ 3,4\} \in A$ Hence {3, 4} $ \subset $ A is incorrect.
View full question & answer→Question 1191 Mark
{x : x is an even natural number less than 6} $\subset$ {x : x is a natural number which divides 36}
View full question & answer→Question 1201 Mark
{a} $\in$ {a, b, c}
View full question & answer→Question 1211 Mark
{a} $\in$ {a, b, c}
View full question & answer→Question 1221 Mark
{a} $\subset$ {a, b, c}
View full question & answer→Question 1231 Mark
{ 1, 2, 3 } $⊂$ { 1, 3, 5 }
View full question & answer→Question 1241 Mark
{a, e} $\subset$ { x, x is a vowel in the English alphabet}
View full question & answer→Question 1251 Mark
{ a, b } $⊄$ { b, c, a }
View full question & answer→Question 1261 Mark
Make correct statement by filling the symbol $\subset$ or $\not\subset$ in the blank space: {x : x is an even natural number} {x : x is an integer}
Answer{x : x is an even natural number} $\subset$ {x : x is an integer}
View full question & answer→Question 1271 Mark
Make correct statement by filling the symbol $\subset$ or $\not\subset$ in the blank space: {x : x is an equilateral triangle in a plane} {x : x is a triangle in the same plane}
Answer{x : x is an equilateral triangle in a plane} $\subset$ {x: x is a triangle in the same plane}
View full question & answer→Question 1281 Mark
Make correct statement by filling the symbol $\subset$ or $\not\subset$ in the blank space: {x: x is a triangle in a plane}......... {x : x is a rectangle in the same plane}
Answer{x : x is a triangle in a plane} $\not\subset$ {x : x is a rectangle in the plane}
View full question & answer→Question 1291 Mark
Make correct statement by filling the symbol $\subset$ or $\not\subset$ in the blank space: {x : x is a circle in the plane}.......{x : x is a circle in the same plane with radius 1 unit}
Answer{x : x is a circle in the plane} $\not\subset$ {x : x is a circle in the same plane with radius 1 unit}
View full question & answer→Question 1301 Mark
Make correct statement by filling the symbol $\subset$ or $\not\subset$ in the blank space: {x : x is a student of Class XI of your school} ....... {x : x student of your school}
Answer{x : x is a student of Class XI of your school} $\subset$ {x : x student of your school}
View full question & answer→Question 1311 Mark
Make correct statement by filling the symbol $\subset$ or $\not\subset$ in the blank space: {a, b, c} . . . {b, c, d}
Answer{a, b, c} $\not\subset$ {b, c, d}
View full question & answer→Question 1321 Mark
Make correct statement by filling the symbol $\subset$ or $\not\subset$ in the blank space: {2, 3, 4}. . . {1, 2, 3, 4, 5}
Answer{2, 3, 4} $\subset$ {1, 2, 3, 4, 5}
View full question & answer→Question 1331 Mark
From the sets given below, select equal sets:
A = {2, 4, 8, 12}, B = {1, 2, 3, 4}, C = {4, 8, 12, 14}, D = {3, 1, 4, 2}, E = {-1,1}, F = {0, a}, G = {1,-1}, H = {0, 1}
AnswerFrom the given sets, we see that sets B and D have same elements and also sets E and G have same elements. $\therefore$ B = D = {1, 2, 3, 4} and E = G = {-1,1}
View full question & answer→Question 1341 Mark
Is pair of set A = {x : x is a letter of the word FOLLOW} and B = {x : x is a letter of the word WOLF} equal? Give reasons.
AnswerA = {F, O, L, W}
B = {W, O, L, F} [repetition is not allowed]
= {W, O, L, F} [The order in which the elements are written does not matter]
Hence, A = B
View full question & answer→Question 1351 Mark
Is the pair of set A = {2, 3} and B = {x : x is solution of x2 + 5x + 6 = 0} equal? Give reasons.
AnswerA = {2, 3} and B = {x : x is solution of x2 + 5x + 6 = 0}
Now x2 + 5x + 6 = 0 $\Rightarrow$ x2 + 3x + 2x + 6 = 0
$\Rightarrow$ (x + 3)(x + 2) = 0 $\Rightarrow$ x = -3, -2
$\therefore$ B = {-2, -3}
Hence A and B are not equal sets.
View full question & answer→Question 1361 Mark
State whether A = B or not if set A = {x : x is a multiple of 10} and set B = {10, 15, 20, 25, 30, . . .}
AnswerA = {x : x is a multiple of 10} can be written in roster form as A = {10, 20, 30, 40, . . .} and B = {10, 15, 20, 25,30, . . .} are not equal sets because $15 \in B,15 \notin A$
View full question & answer→Question 1371 Mark
State whether A = B or not if set A = {2, 4, 6, 8, 10} and set B = {x: x is a positive even integer and $x \leq 10$}
AnswerA= {2, 4, 6, 8, 10} and B = {x : x is a positive even integer and $x \leq 10$} which can be written in roster form as B = {2, 4, 6, 8, 10} are equal sets.
$\therefore$ A = B = {2, 4, 6, 8, 10}
View full question & answer→Question 1381 Mark
State whether A = B or not if set A = {4, 8, 12, 16} and set B = {8, 4, 16, 18}
AnswerA = {4, 8, 12, 16} and B= {8, 4, 16, 18} are not equal sets because $12 \in A,12 \notin B$and $18 \in B,18 \notin A$
View full question & answer→Question 1391 Mark
State whether A = B or not if set A = {a, b, c, d} and set B = {d, c, b, a}
AnswerA = {a, b, c, d} and B = {d, c, b, a} are equal sets because order of elements does not change a set. $\therefore$ A = B = {a, b, c, d}
View full question & answer→Question 1401 Mark
Is the set of circles passing through the origin (0, 0) finite or infinite?
AnswerThe set of circles passing through the origin (0, 0) is an infinite set because we can draw infinite number of circles through origin of different radii.
View full question & answer→Question 1411 Mark
Is the set of animals living on the earth finite or infinite?
AnswerThe set of animals living on the earth is a finite set because the number of animals living on the earth is very large but finite.
View full question & answer→Question 1421 Mark
Is the set of numbers which are multiples of 5 finite or infinite?
AnswerThe set of numbers which are multiple of 5 is an infinite set because there are infinite multiples of 5.
View full question & answer→Question 1431 Mark
Is the set of letters in the English alphabet finite or infinite?
AnswerThe set of letters in the English alphabet is a finite set because there are 26 letters in the English alphabet.
View full question & answer→Question 1441 Mark
Is the set of lines which are parallel to the x-axis finite or infinite?
AnswerThe set of lines which are parallel to the x-axis is an infinite set because we can draw infinite number of lines parallel to x-axis.
View full question & answer→Question 1451 Mark
Is the set of prime numbers less than 99 finite or infinite?
AnswerThe set of prime numbers less than 99 is a finite set because the set contains finite number of elements.
View full question & answer→Question 1461 Mark
Is the set of positive integers greater than 100 finite or infinite set?
AnswerThe set of positive integers greater than 100 is an infinite set because there are infinite number of positive integers greater than 100.
View full question & answer→Question 1471 Mark
Is the set {1, 2, 3, . . . , 99, 100} is finite or infinite?
Answer{1, 2, 3, . . . , 99, 100} is a finite set because the set contains finite number of elements.
View full question & answer→Question 1481 Mark
Is the set {1, 2, 3, ............... } is finite or infinite?
Answer{1, 2, 3, . . . }is an infinite set because there are infinite elements in the set.
View full question & answer→Question 1491 Mark
Is the set of months of a year is a finite or infinite set?
AnswerThe set of months of a year is a finite set because there are 12 months in a year.
View full question & answer→Question 1501 Mark
Is y : y is a point common to any two parallel lines null set?
Answer{x : x is a point common to any two parallel lines} is an empty set because two parallel lines do not have a common point.
View full question & answer→Question 1511 Mark
Is x : x is a natural number, x < 5 and, x > 7 null set?
Answer{x : x is a natural number, x< 5 and x > 7} is an empty set because there is no natural number which satisfies simultaneously r < 5 and x > 7.
View full question & answer→Question 1521 Mark
Is set of even prime numbers null set?
AnswerSet of even prime numbers is {2} which is not empty set.
View full question & answer→Question 1531 Mark
Is set of odd natural numbers divisible by 2 null set?
AnswerHere, Set of odd natural numbers divisible by 2.
As we know that a set is a collection of well defined distnict objects.
Let we represent the given set in roaster form:
$⇒$ Set of odd natural numbers divisible by 2 is $\phi$
Because no odd natural number can be divided by 2. Therefore, it is a null set.
View full question & answer→Question 1541 Mark
List the element of the set: E = {x : x is a month of a year not having 31 days}
AnswerE = {x : x is a month of a year not having 31 days}
$\therefore$ E = {February, April, June, September, November}
View full question & answer→Question 1551 Mark
List the element of the set: C = {x : x is an integer, ${x^2} \leq 4$}
AnswerC = {x : x is an integer, ${x^2} \leq 4$}
$\therefore {x^2} \leq 4 \Rightarrow x \leq \pm 2$ $ \Rightarrow - 2 \leq x \leq 2$
$\therefore C = ( - 2, - 1,0,1,2)$
View full question & answer→Question 1561 Mark
List the element of the set: C = {x : x is an integer, $\frac{1}{2}<x<\frac{9}{2}$}
AnswerB = (x : x is an integer, $ - 1/2 < x < 9/2$)
$\therefore$ B = {0, 1, 2, 3, 4}
View full question & answer→Question 1571 Mark
Write the set in the set-builder form: {1, 4, 9, . . . , 100}
AnswerLet E = {1, 4, 9, ....., 100}
All objects ofthe set are perfect squares.
$\therefore D = \{ x:x = {n^2}\,and\,\,1 \leqslant n \leqslant 10\} $
View full question & answer→Question 1581 Mark
Write the set in the set-builder form: {5, 25, 125, 625}
AnswerLet C = {5, 25, 125, 625}
All objects of the set are natural numbers that are powers of 5.
$\therefore C = \{ x:x = {5^n},n \in N\,and\,\,1 \leqslant n \leqslant 4\} $
View full question & answer→Question 1591 Mark
Write the set in the set-builder form: {2, 4, 8, 16, 32}
AnswerLet B = {2, 4,8,16,32}
All objects of the set are natural numbers that are powers of 2.
$\therefore B = \{ x:x = {2^n},n \in N\,and\,\,1 \leqslant n \leqslant 5\} $
View full question & answer→Question 1601 Mark
Write the set in roster form: F = The set of all letters in the word BETTER.
AnswerF = The set of all letters in the word BETTER
$\therefore F$ = {B, E, T, R}
View full question & answer→Question 1611 Mark
Write the set in roster form: E = The set of all letters in the word TRIGONOMETRY
AnswerE = The set of all letters in the word TRIGONOMETRY
$\therefore E$ = {T, R, I, G, O, N, M, E, Y}
View full question & answer→Question 1621 Mark
Write the set in roster form: D = {x : x is a prime number which is divisor of 60}
AnswerD = {x : x is a prime number which is divisor of 60}
$\therefore D$ = {2,3, 5}
View full question & answer→Question 1631 Mark
Write the set in roster form: C = {x : x is a two-digit natural number such that the sum of its digits is 8}
AnswerC = {x : x is a two-digit natural number such that the sum of its digit is 8}
$\therefore$ C = {17, 26, 35, 44, 53, 62, 71, 80}
View full question & answer→Question 1641 Mark
Is the collection of most dangerous animals of the world set? Justify your answer.
AnswerA collection of most dangerous animals of the world is not a very clearly defined set as the ranking of the animals keep on altering and their ranking vary from countries to countries.
The collection of distnict objects are not well–defined and don't have universal acceptance as it is.
Therefore,the collection is not set.
View full question & answer→Question 1651 Mark
Is a collection of novels written by the writer Munshi Prem Chand set? Justify your answer
AnswerWe will to explain a collection of novels written by the writer Munshi Prem Chand is a well-defined collection because there are finite numbers of books which Munshi Prem Chand has written. The names of the book could not vary from person to person on the basis of personal choice. The well-defined objects of the collection make it a set.
Therefore, this collection is a set.
View full question & answer→Question 1661 Mark
Is the collection of all the months of a year beginning with the letter J set? Justify your answer
AnswerSet: Collection of well defined and distnict objects.
There are three months of a year which begins with the letter J, rest of the month`s name begin with different letter. Therefore, the given collection has well-defined and distnict objects namely January, June and July.
Therefore, this collection is a set.
{x: x = months of a year beginning with letter J}
Alternatively
{x: x = January, June, July where January, June, July are month of a year}
View full question & answer→Question 1671 Mark
Consider the sets $\phi$, A = { 1, 3 }, B = {1, 5, 9}, C = {1, 3, 5, 7, 9}. Insert the symbol $⊂ or ⊄$ between the pair of sets: B . . . C
AnswerB $⊂$ C as each element of B is also an element of C.
View full question & answer→Question 1681 Mark
Consider the sets $\phi$, A = { 1, 3 }, B = {1, 5, 9}, C = {1, 3, 5, 7, 9}. Insert the symbol $⊂ or ⊄$ between the pair of set: A . . . C
AnswerSince A $⊂$ C as 1, 3 $∈$ A also belongs to C
View full question & answer→Question 1691 Mark
Consider the sets $\phi$, A = { 1, 3 }, B = {1, 5, 9}, C = {1, 3, 5, 7, 9}. Insert the symbol $⊂ or ⊄$ between the pair of set: A . . . B
AnswerA $⊄$ B as 3 $∈$ A and 3 $∉$ B
View full question & answer→Question 1701 Mark
Consider the sets $\phi$, A = { 1, 3 }, B = {1, 5, 9}, C = {1, 3, 5, 7, 9}. Insert the symbol $⊂ or ⊄$ between the pair of set: $\phi$ . . . B
AnswerWe have, $\phi ⊂$ B as $\phi$ is a subset of every set
View full question & answer→Question 1711 Mark
Show that the given set that is A = {n : n $\in$ Z and n2 ≤ 4} and B = {x : x $\in$ R and x2 – 3x + 2 = 0} are equal or not? Justify your answer.
AnswerA = {–2, –1, 0, 1, 2}, B = {1, 2}. Since 0 $\in$ A and 0 $\notin$ B, hence Aand B are not equal sets.
View full question & answer→Question 1721 Mark
Show that the given set that is X, the set of letters in “ALLOY” and B, the set of letters in “LOYAL” are equal? Justify your answer.
AnswerGiven, X = {A, L, L, O, Y}, B = {L, O, Y, A, L}. Then X and B are equal sets as repetition of elements in a set do not change a set.
Therefore ,X = {A, L, O, Y} = B
View full question & answer→Question 1731 Mark
Is the set {x : x $\in$ N and x is odd} finite or infinite?
AnswerSince there are infinite number of odd numbers, therefore, the given set is infinite.
View full question & answer→Question 1741 Mark
Is the set {x: x $\in$ N and x is prime} finite or infinite?
AnswerThe given set is the set of all prime numbers and since set of prime numbers is infinite. Therefore, the given set is infinite.
View full question & answer→Question 1751 Mark
Is the set {x : x $\in$ N and 2x –1 = 0} finite or infinite?
AnswerGiven set = $\phi$. Therefore, this is finite.
View full question & answer→Question 1761 Mark
Is the set {x : x $\in$ N and x2 = 4} finite or infinite?
AnswerGiven set = {2}. Thus, it is finite.
View full question & answer→Question 1771 Mark
Is the set {x : x $\in$ N and (x – 1) (x – 2) = 0} finite or infinite?
AnswerWe have the set = {1, 2}. Hence, it is finite.
View full question & answer→Question 1781 Mark
Match each of the set on the left described in the roster form with the same set on the right described in the set-builder form :
| (a) {P, R, I, N, C, A, L} | (i) { x : x is a positive integer and is a divisor of 18} |
| (b) {0} | (ii) { x : x is an integer and x2 – 9 = 0} |
| (c) {1, 2, 3, 6, 9, 18} | (iii) {x : x is an integer and x + 1 = 1} |
| (d) {3, –3} | (iv) {x : x is a letter of the word PRINCIPAL} |
Question 1791 Mark
Write the set $\left[\frac{1}{2}, \frac{2}{3}, \frac{3}{4}, \frac{4}{5}, \frac{5}{6}, \frac{6}{7}\right]$ in the set-builder form.
AnswerHere,we see that each member in the given set has the numerator one less than the denominator. Also, the numerator begin from 1 and do not exceed 6.
Therefore, in the set-builder form the given set is {x : x = $\frac{n}{n+1}$, here n is a natural number and 1 $\leq$ n $\leq$ 6}
View full question & answer→Question 1801 Mark
Write the set A = {1, 4, 9, 16, 25, . . . }in set-builder form.
AnswerWe have, A = {x : x is the square of a natural number}
Alternatively, we can write A = {x : x = n2 , where n $\in$ N}
View full question & answer→Question 1811 Mark
List all the subsets of the set { –1, 0, 1}
AnswerSuppose A = { –1, 0, 1}.
Now, we have to calculate all the subset of A having no element is the empty set $\phi$.
The subsets of A having one element are { –1}, {0}, {1}.
The subsets of
A having two elements are {–1, 0}, {–1, 1} ,{0, 1}.
The subset of A having three elements of A is A itself.
Therefore, all the subsets of A are $\phi$, {–1}, {0}, {1}, {–1, 0}, {–1, 1}, {0, 1} and {–1, 0, 1}
View full question & answer→Question 1821 Mark
There are 200 individual with a skin disorder, 120 has been exposed to chemical C1, 50 to chemical C2 and 30 to both the chemicals C1 and C2. Find the number of individual exposed to chemical C1 or chemical C2
AnswerThe number of individuals exposed to chemical C1 or chemical $C_2$ is given by $n(A \cup B).$
Now, we have, $n (A\cup B) = n(A) + n(B) - n(A\cap B)$
$= 120 + 50 - 30$
$= 140$
Therefore, required number of individuals is $140$
View full question & answer→Question 1831 Mark
There are 200 individual with a skin disorder, 120 has been exposed to chemical C1, 50 to chemical C2 and 30 to both the chemicals C1 and C2. Find the number of individual exposed to chemical C2 but not chemical C1
AnswerThe number of individuals exposed to chemical C2 but not chemical $C_1$ is given by $n(\overline A\cap B$).
Now, we have n( $\overline A \cap$ B) $= n (B) - n(A\cap B)$
$= 50 - 30$
$= 20$
Therefore, required number is $20.$
View full question & answer→Question 1841 Mark
There are 200 individual with a skin disorder, 120 has been exposed to chemical C1, 50 to chemical C2 and 30 to both the chemicals C1 and C2. Find the number of individual exposed to chemical C1 but not chemical C2
AnswerThe number of individuals exposed to chemical $C_1$ but not chemical $C_2$ is given by $n (A\cap \overline B).$
Now, we have n(A $\cap \overline B$) $= n(A) - n(A\cap B)$
$= 120 - 30$
$= 90$
Therefore, required number of individuals is $90$
View full question & answer→Question 1851 Mark
Write the set {x : x is a positive integer and x2 < 40} in the roster form.
AnswerThe required numbers are 1, 2, 3, 4, 5, 6. Therefore, the given set in the roster form is {1, 2, 3, 4, 5, 6}.
View full question & answer→Question 1861 Mark
Let V = { a, e, i, o, u } and B = { a, i, k, u}. Find V – B and B – V
AnswerHere ,it is V - B = {e, o}, since the elements e, o belongs to V but not to B and B - V = { k }, since the element k belongs to B but not to V
View full question & answer→Question 1871 Mark
Let A = { 1, 2, 3, 4, 5, 6}, B = { 2, 4, 6, 8 }. Find A – B and B – A.
AnswerHere, A - B = {1, 3, 5}, since the elements 1, 3, 5 belong to A but not to B and also B - A = {8}, since the element 8 belongs to B and not to A.then,
We note that A - B $\ne$ B – A
View full question & answer→Question 1881 Mark
Let X = {Ram, Geeta, Akbar} be the set of students of Class XI, who are in school hockey team. Let Y = {Geeta, David, Ashok} be the set of students from Class XI who are in the school football team. Find X $\cap$ Y and interpret the set
AnswerWe see that element ‘Geeta’ is the only element common to both. Therefore, X $\cap$ Y = {Geeta}
View full question & answer→Question 1891 Mark
Let A = { 2, 4, 6, 8} and B = { 6, 8, 10, 12}. Find A $\cap$ B
AnswerWe see that 6, 8 are the only elements which are common to both A and B.
Therefore,A $\cap$ B = { 6, 8 }
View full question & answer→Question 1901 Mark
Let X = {Ram, Geeta, Akbar} be the set of students of Class XI, who are in school hockey team. Let Y = {Geeta, David, Ashok} be the set of students from Class XI who are in the school football team. Find X $\cup$ Y and interpret the set.
AnswerHere, X $\cup$ Y = {Ram, Geeta, Akbar, David, Ashok}. So,this is the set of students from Class XI who are in the hockey team or the football team or both.
View full question & answer→Question 1911 Mark
Let A = { a, e, i, o, u } and B = { a, i, u }. Show that A $\cup$ B = A
AnswerWe have, A $\cup$ B = { a, e, i, o, u } = A.
This example illustrates that union of sets A and its subset B is the set A We know that if B $\subset$ A, then A $\cup$ B = A.
View full question & answer→Question 1921 Mark
Let A = { 2, 4, 6, 8} and B = { 6, 8, 10, 12}. Find A $\cup$ B
AnswerIt is given that A = { 2, 4, 6, 8} and B = { 6, 8, 10, 12}
$\therefore$ We have A $\cup$ B = { 2, 4, 6, 8, 10, 12}
View full question & answer→Question 1931 Mark
Let A, B and C be three sets. If A $∈$ B and B $⊂$ C, is it true that A $⊂$ C ? If not, give an example.
AnswerWe know that an element of a set can never be a subset of itself.
Suppose A = {1}, B = {{1}, 2} and C = {{1}, 2, 3}.
Here A $∈$ B as A = {1} and B $⊂$ C. But A $⊄$ C as 1 $∈$ A and 1 $∉$ C.
View full question & answer→Question 1941 Mark
Let A = {a, e, i, o, u} and B = {a, b, c, d}. Is A a subset of B? No. (Why?). Is B a subset of A?
Answer - Is A $\begin{equation} \subset \end{equation}$ B
According to the given we can state,
For a set to be a subset of another set, it needs to have all element presents in another set. In the set A = {e, i, o, u} elements are present but these are not present in set B.
Hence A $\begin{equation} \not \subset \end{equation}$ B - Is b $\begin{equation} \subset \end{equation}$ A
According to the given we can state,
For this condition to be true, are elements of sets B should be element present in sets A.
In the set B = {b, c, d} elements are present but these elements are not an element in set A.
Hence B $\begin{equation} \not \subset \end{equation}$ A
View full question & answer→Question 1951 Mark
Write the solution set of the equation x2 + x – 2 = 0 in roster form.
Answer Here,the given equation can be written as -
(x – 1) (x + 2) = 0, that is x = 1, – 2
Therefore, the solution set of the given equation can be written in roster form as {1, – 2}.
View full question & answer→