If $A = (6, 7, 8, 9), B = (4, 6, 8, 10)$ and $C = \{x : x \in N : 2 < x ≤ 7\} ;$ find $: B − C$
- A$\{4, 6\}$
- B$\{4, 6, 8\}$
- C$\{6, 8, 10\}$
- ✓$\{8, 10\}$
Answer: D.
View full solution →Question types
Sets question types
428 questions across 7 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
428
Questions
7
Question groups
5
Question types
01
M.C.Q (1 Marks)
175 Q→02Assertion (A) & Reason (B) MCQ
15 Q→03True False[1 Marks ]
7 Q→041 Marks Question
195 Q→052 Marks Questions
18 Q→063 Marks Question
12 Q→07Case study (4 Marks)
6 Q→Sample Questions
Sets questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
How many elements has $P(A),$ if $A = f ?$
- ATwo
- ✓One
- CThree
- DZero.
Answer: B.
View full solution →In a class of $50$ students, $10$ did not opt for math, $15$ did not opt for science and $2$ did not opt for either. How many students of the class opted for both math and science.
- A$24$
- B$25$
- C$26$
- ✓$27$
Answer: D.
View full solution →The set $\text{(A}\cup\text{B}')'\cup\text{B}\cap\text{C}$ is equal to:
- A$\text{A}'\cup\text{B}\cup\text{C}$
- ✓$\text{A}'\cup\text{B}$
- C$\text{A}'\cup\text{C}'$
- D$\text{A}'\cap\text{B}.$
Answer: B.
View full solution →The cardinality of the set $P(P(P(f)))$ is.
- A$0$
- B$1$
- C$2$
- ✓$4$
Answer: D.
View full solution →Directions: In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R).$ Mark the correct choice as:
Assertion: If $\text{A}\subset\text{B}$ for any two sets $A$ and $B.$
Then, above Venn diagram represents correct relationship between $A$ and $B.$
Reason: If $\text{A}\subset\text{B},$ then all elements of $A$ is also in $B.$
Assertion: If $\text{A}\subset\text{B}$ for any two sets $A$ and $B.$
Then, above Venn diagram represents correct relationship between $A$ and $B.$
Reason: If $\text{A}\subset\text{B},$ then all elements of $A$ is also in $B.$
- A$A$ is true, $R$ is true; $R$ is a correct explanation of $A.$
- B$A$ is true, $R$ is true; $R$ is not a correct explanation of $A.$
- C$A$ is true; $R$ is false.
- ✓$A$ is false; $R$ is true.
Answer: D.
View full solution →Directions: In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R).$ Mark the correct choice as:
Assertion: The set $D = \{x : x$ is a prime number which is a divisor of $60\}$ in roster form is $\{1, 2, 3, 4, 5\}.$
Reason: The set $E =$ the set of all letters in the word $‘\text{TRIGONOMETRY}’,$ in the roster form is $\text{\{T, R, I, G, O, N, M, E, Y\}}.$
Assertion: The set $D = \{x : x$ is a prime number which is a divisor of $60\}$ in roster form is $\{1, 2, 3, 4, 5\}.$
Reason: The set $E =$ the set of all letters in the word $‘\text{TRIGONOMETRY}’,$ in the roster form is $\text{\{T, R, I, G, O, N, M, E, Y\}}.$
- A$A$ is true, $R$ is true; $R$ is a correct explanation of $A.$
- B$A$ is true, $R$ is true; $R$ is not a correct explanation of $A.$
- C$A$ is true; $R$ is false.
- ✓$A$ is false; $R$ is true.
Answer: D.
View full solution →Directions: In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R)$. Mark the correct choice as:
Assertion: The set $A = \{x : x$ is an even prime number greater than $2\}$ is the empty set.
Reason: The set $B = \{x : x^2 = 4, x$ is odd$\} $ is not an empty set.
Assertion: The set $A = \{x : x$ is an even prime number greater than $2\}$ is the empty set.
Reason: The set $B = \{x : x^2 = 4, x$ is odd$\} $ is not an empty set.
- A$A $ is true, $R$ is true; $R$ is a correct explanation of $A.$
- B$A$ is true, $R$ is true; $R$ is not a correct explanation of $A$.
- ✓$A $ is true; $R$ is false.
- D$A$ is false; $R$ is true.
Answer: C.
View full solution →Directions: In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R).$ Mark the correct choice as:
Assertion: If $n(A) = 3, n(B) = 6$ and $\text{A}\subset\text{B},$ then the number of elements in $\text{A}\cup\text{B}$ is $9.$
Reason: If $A$ and $B$ are disjoint, then $\text{n}(\text{A}\cup\text{B})$ is $\text{n(A) + n(B).}$
Assertion: If $n(A) = 3, n(B) = 6$ and $\text{A}\subset\text{B},$ then the number of elements in $\text{A}\cup\text{B}$ is $9.$
Reason: If $A$ and $B$ are disjoint, then $\text{n}(\text{A}\cup\text{B})$ is $\text{n(A) + n(B).}$
- A$A$ is true, $R$ is true; $R$ is a correct explanation of $A.$
- B$A$ is true, $R$ is true; $R$ is not a correct explanation of $A.$
- C$A$ is true; $R$ is false.
- ✓$A$ is false; $R$ is true.
Answer: D.
View full solution →Directions: In the following questions, a statement of assertion $(A)$ is followed by a statement of reason $(R).$ Mark the correct choice as:
Assertion: The interval $\{\text{x}:\text{x}\in\text{R},-4<\text{x}\leq6\}$ is represented by $(-4, 6).$
Reason: The interval $\{\text{x}:\text{x}\in\text{R}, -12 -4 < x < 10\}$ is represented by $[-12, -10].$
Assertion: The interval $\{\text{x}:\text{x}\in\text{R},-4<\text{x}\leq6\}$ is represented by $(-4, 6).$
Reason: The interval $\{\text{x}:\text{x}\in\text{R}, -12 -4 < x < 10\}$ is represented by $[-12, -10].$
- A$A$ is true, $R$ is true; $R$ is a correct explanation of $A.$
- B$A$ is true, $R$ is true; $R$ is not a correct explanation of $A.$
- ✓$A$ is true; $R$ is false.
- D$A$ is false; $R$ is true.
Answer: C.
View full solution →If A $\subset$ B and x $\notin$ B, then x $\notin$ A. If it is true, prove it. If it is false, give an example.
View full solution →If x $\in$ A and A $\not \subset$ B , then x $\in$ B. If it is true, prove it. If it is false, give an example.
View full solution →If $A \not \subset B$ and $B \not \subset C$ , then $A \not \subset C$. If it is true, prove it. If it is false, give an example.
View full solution →If $A \not \subset B$ and $B \not \subset C$ , then $A \not \subset C$. If it is true, prove it. If it is false, give an example.
View full solution →If A $\subset$ B and B $\subset$ C , then A $\subset$ C. If it is true, prove it. If it is false, give an example.
View full solution →Using properties of sets, show that: $A \cap (A \cup B) = A$
View full solution →Using properties of set, show that: $A \cup (A \cap B) = A$
View full solution →Show that if $A \subset B$ then $C - B \subset C - A.$
View full solution →Show that $A \cap B = A \cap C$ need not imply B = C.
View full solution →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 ${A'}$?
View full solution →Is it true that for any sets A and B, $P(A) \cup P(B) = P(A \cup B)?$Justify your answer.
View full solution →Assume that P(A) = P(B) show that A = B.
Let A, B and C be the sets such that $A \cup B = A \cup C$ and $A \cap B = A \cap C$ Show that B = C.
View full solution →In a survey of 60 people, it was found that 25 people read newspaper H, 26 read newspaper T, 26 read newspaper I, 9 read both H and I, 11 read both H and T, 8 read both T and I, 3 read all three newspapers.
Find the number of people who read exactly one newspaper.
Find the number of people who read exactly one newspaper.
In a survey of 60 people, it was found that 25 people read newspaper H, 26 read newspaper T, 26 read newspaper I, 9 read both H and I, 11 read both H and T, 8 read both T and I, 3 read all three newspapers.
Find the number of people who read at least one of the newspaper.
Find the number of people who read at least one of the newspaper.
Show that for any sets A and B, A = ( A $\cap$ B ) $\cup$ ( A – B ) and A $\cup$ ( B – A ) = ( A $\cup$ B )
View full solution →Show that the following four conditions are equivalent :
View full solution →- $A \subset B$
- $A – B = \phi$
- $A \cup B = B$
- $A \cap B = A$
In a survey it was found that 21 people liked product A, 26 liked product B and 29 liked product C. If 14 people liked products A and B, 12 people liked products C and A, 14 people liked products B and C and 8 liked all the three products. Find how many liked product C only?
Let A and B are sets. If $A \cap X = B \cap X = \phi $ and $A \cup X = B \cup X$ for some set X. Show that A = B.
[Hints A = A $\cap$ ( A $\cup$ X ) , B = B $\cap$ ( B $\cup$ X ) and use Distributive law ]
View full solution →[Hints A = A $\cap$ ( A $\cup$ X ) , B = B $\cap$ ( B $\cup$ X ) and use Distributive law ]
Decide among the following sets which sets are subsets of each another:
A = {X : X $\in$ R} and x satisfies x2 - 8x + 12 = 0}, B = {2, 4, 6} , C = {2, 4, 6, 8, ...}, D = {6}
View full solution →A = {X : X $\in$ R} and x satisfies x2 - 8x + 12 = 0}, B = {2, 4, 6} , C = {2, 4, 6, 8, ...}, D = {6}
A class teacher Mamta Sharma of class $XI$ write three sets $A, B$ and Care such that $A = \{1, 3, 5, 7, 9\}, B = \{2, 4, 6, 8\}$ and $C = \{2, 3, 5, 7, 11\}.$
Answer the following questions which are based on above sets.
View full solution →Answer the following questions which are based on above sets.
- Find $\text{A}\cap\text{B}.$
- $\{3, 5, 7\}$
- $\phi$
- $\{1, 5, 7\}$
- $\{2, 5, 7\}$
- Find $\text{A}\cap\text{C}.$
- $\{3, 5, 7\}$
- $\{1, 5, 7\}$
- $\phi$
- $\{3, 4, 7\}$
- Which of the following is correct for two sets $A$ and $B$ to be disjoint?
- $\text{A}\cap\text{B}=\phi$
- $\text{A}\cap\text{B}\neq\phi$
- $\text{A}\cup\text{B}=\phi$
- $\text{A}\cup\text{B}\neq\phi$
- Which of the following is correct for two sets $A$ and $C$ to be intersecting?
- $\text{A}\cap\text{C}=\phi$
- $\text{A}\cap\text{C}\neq\phi$
- $\text{A}\cup\text{C}=\phi$
- $\text{A}\cup\text{C}\neq\phi$
- Write the $n[P(B)].$
- $8$
- $4$
- $16$
- $12$
The school organised a farewell party for $100$ students and school management decided three types of drinks will be distributed in farewell party ie. Milk $(M),$ Coffee $(C)$ and Tea $(T)$. Organiser reported that $10$ students had all the three drinks $M, C, T. 20$ students had $M$ and $C; 30$ students had $C$ and $T; 25$ students had $M$ and $T. 12$ students.had $M$ only; $5$ students had $C$ only; $8$ students had $T$ only.
Based on the above information, answer the following questions.
View full solution →Based on the above information, answer the following questions.
- The number of students who did not take any drink, is
- $20$
- $30$
- $10$
- $25$
- The number of students who prefer Milk is
- $47$
- $45$
- $53$
- $50$
- The number of students who prefer Coffee is
- $47$
- $53$
- $45$
- $50$
- The number of students who prefer Tea is
- $51$
- $53$
- $50$
- $47$
- The number of students who prefer Milk and Coffee but not tea is
- $12$
- $10$
- $15$
- $20$
In a library, $25$ students read physics, chemistry and mathematics books. It was found that $15$ students read mathematics, $12$ students read physics while $11$ students read chemistry. $5$ students read both mathematics and chemistry, $9$ students read physics and mathematics. $4$ students read physics and chemistry and $3$ students read all three subject books.
Based on the above information, answer the following questions.
View full solution →Based on the above information, answer the following questions.
- The number of students who reading only chemistry is:
- $5$
- $4$
- $2$
- $1$
- The number of students who reading only mathematics is:
- $4$
- $3$
- $5$
- $11$
- The number of students who reading only one of the subjects is:
- $5$
- $11$
- $8$
- $6$
- The number of students who reading atleast one of the subject is:
- $20$
- $22$
- $23$
- $21$
- The number of students who reading none of the subject is:
- $2$
- $4$
- $3$
- $5$
In a company, $100$ employees offered to do a work. In out of them, $10$ employees offered ground floor only, $15$ employees offered first floor only, $10$ employees offered second floor only, $30$ employees offered second floor and ground floor to work, $25$ employees offered first and second floor, $15$ employees offered ground and first floor, $60$ employees offered second floor.
Based on the above information answer the following questions.
View full solution →Based on the above information answer the following questions.
- The number of employees who offered all three floors.
- $5$
- $3$
- $4$
- $6$
- The number of employees who offered ground floor.
- $50$
- $60$
- $65$
- $70$
- The number of employees who offered first floor.
- $40$
- $45$
- $50$
- $55$
- The number of employees who offered ground and first floor but not second floor.
- $10$
- $15$
- $20$
- $25$
- The number of employees who did not offer any of the above three floors.
- $15$
- $10$
- $5$
- $0$
In an University, out of $100$ students $15$ students offered Mathematics only, $12$ students offered Statistics only, $8$ students offered only Physics, $40$ students offered Physics and Mathematics, $20$ students offered Physics and Statistics, $10$ students offered Mathematics and Statistics, $65$ students offered Physics.
Based on the above information answer the following questions.
View full solution →Based on the above information answer the following questions.
- The number of students who offered all the three subjects is:
- $4$
- $3$
- $2$
- $5$
- The number of students who offered Mathematics is:
- $62$
- $65$
- $55$
- $60$
- The number of students who offered statistics is:
- $31$
- $35$
- $39$
- $34$
- The number of students who offered mathematics and statistics but not physics is:
- $7$
- $6$
- $5$
- $4$
- The number of students who did not offer any of the above three subjects is:
- $4$
- $1$
- $5$
- $3$
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