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 = 2^0 = 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 $B=\left\{x: x\right.$ is solution of $\left.x^2+5 x+6=0\right\}$ equal? Give reasons.
Answer$A=\{2,3\}$ and $B=\left\{x: x\right.$ is solution of $\left.x^2+5 x+6=0\right\}$
Now $x^2+5 x+6=0 \Rightarrow x^2+3 x+2 x+6=0$
$\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→