Sample QuestionsSets questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
If A and B are two sets such that $\text{n(A)}=70, \text{ n(B)}=60, \text{ n(A}\cup\text{B)}=110,$ then $\text{n(A}\cap\text{B)}$ is equal to:
Answer: D.
View full solution →Let $\text{A} = \{\text{x : x} \in \text{R}, \text{x > 4}\}$ and $\text{B}= \{\text{x}\in\text{R : x} < 5\}.$ Then, $\text{A}\cap\text{B}=$
Answer: C.
View full solution →For any two sets A and B, $\text{A}\cap\text{(A}\cup\text{B)}=$
Answer: A.
View full solution →If A = {1, 3, 5, B} and B = {2, 4}, then:
Answer: D.
View full solution →Let A and B be two sets that $\text{n(A)} = 16, \text{ n(B)} = 14,\text{ n(A}\cup\text{B)}=25.$ Then, $\text{n(A}\cap\text{B)}$ is equal to:
Answer: C.
View full solution →Show that the set of letters needed to spell "CATARACT" and the set of letters needed to spell "TRACT" are equal?
Write down the all possible subset of the given set. {a, b, c}
Describe the following sets in set-builder form: {5, 25, 125 625};
If $A=\left\{x \in C: x^2=1\right\}$ and $B=\left\{x \in C: x^4=1\right\}$, then write $A-B$ and $B-A$.
View full solution →Write down the all possible subset of the given set. {a}.
Find the smallest set A such that $\text{A}\cup\{1, 2\} = \{1, 2, 3, 5, 9\}.$
View full solution →Describe the following sets in Roster form: {x : x is a two digit number such that the sum of its digits is 8}
If $A = \{1, 2, 3, 4, 5\}, B = \{4, 5, 6, 7, 8\}, C = \{7, 8, 9, 10, 11\},$ and $D = \{10, 11, 12, 13, 14\}.$ Find: $\text{B}\cup\text{C}\cup\text{D}$
If A = {1, 2, 3, 4, 5}, B = {4, 5, 6, 7, 8}, C = {7, 8, 9, 10, 11}, and D = {10, 11, 12, 13, 14}. Find: $\text{A}\cup\text{B}\cup\text{C}$
View full solution →If A = {1, 2, 3, 4, 5}, B = {4, 5, 6, 7, 8}, C = {7, 8, 9, 10, 11}, and D = {10, 11, 12, 13, 14}. Find: $(\text{A}\cap\text{B})\cap(\text{B}\cap\text{C})$
View full solution →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'
- B'
- $(\text{A}\cap\text{C})'$
- $(\text{A}\cup\text{B})'$
- (A')'
- (B - C)'.
View full solution →Let A = {x : x $\in$ N}, B = {x : x = 2n, n $\in$ N}, C = {x : x = 2n - 1, n $\in$ N} and D = {x : x is a prime natural number}. Find: $\text{B}\cap\text{C}$
View full solution →In a school there are 20 teachers who teach mathematics or physics. Of these, 12 teach mathematics and 4 physics and mathematics. How many teach physics?
Let A = {1, 2, 4, 5}, B = {2, 3, 5, 6}, C = {4, 5, 6, 7}. Verify the following identities: $\text{A}\cap(\text{B}-\text{C})=(\text{A}\cap\text{B})-(\text{A}\cap\text{C})$
View full solution →For any two sets, prove that: $\text{A}\cup(\text{A}\cap\text{B})=\text{A}.$
View full solution →For any two sets A and B, prove the following: $\text{A}\cap\text{(A}'\cup\text{B})=\text{A}\cap\text{B}$
View full solution →For any two sets A and B, prove that $\text{A}\cup(\text{B}-\text{A})=\text{A}\cup\text{B}$
View full solution →For any two sets A and B, prove the following: $\text{A}\cap\text{(A}\cup\text{B})=\phi$
View full solution →For any two sets A and B, prove that $(\text{A}\cap\text{B})-\text{B = A}- \text{B}$
View full solution →For any two sets A and B, prove the following: $\text{A}-\text{(A}-\text{B})=\text{A}\cap\text{B}$
View full solution →