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, $\text{A}\cap\text{B}=$
- A
$(4, 5)$
- B
$(4, 5)$
- ✓
$[4, 5]$
- D
$[4, 5].$
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.
${a, b, c}$
View full solution →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.
${a}.$
View full solution →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:
$\text{B}\cup\text{C}\cup\text{D}$
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:
$\text{A}\cup\text{B}\cup\text{C}$
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 →If A, B, C are three sets such that $\text{A}\subset\text{B},$ then prove that $\text{C} - \text{B}\subset\text{C} - \text{A}.$
View full solution →Show that for any sets A and B,$\text{A}\cup(\text{B}-\text{A})=(\text{A}\cup\text{B})$
View full solution →For any two sets of A and B, prove that:$\text{B}'\subset\text{A}'\Rightarrow\text{A}\subset\text{B.}$
View full solution →For any two sets A and B, prove that
$\text{A}-(\text{A}-\text{B})=\text{A}\cap\text{B}$
View full solution →In a group of 50 persons, 14 drink tea but not coffee and 30 drink tea. Find:
How may drink tea and coffee both.
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 →Let A = {a, b, {c, d}, e}. Then the following statements is false and why?
$\phi\in \text{A}$
View full solution →The given statements is corect? Write a correct form of the given incorrect statements.$\{\text{b, c}\}\subset\{\text{a},\{\text{b, c}\}\}$
View full solution →Write the following statement are true? Justify your answer.
The set of all rectangles is contaied in the set of all squares.
The given statements is correct? Write a correct form of the give incorrect statement.
$\text{a}\subset\{\text{a, b, c}\}$
View full solution →Let A = {{1, 2,3}, {4, 5}, {6, 7, 8}}. Then the following is true or false:
$\{1,2,3\}\subset \text{A}.$
View full solution →If A = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} then insert the appropriate symbol $\in$ or $\not\in$ in the following blanks spaces:
-4 ...... A.
View full solution →If A = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} then insert the appropriate symbol $\in$ or $\not\in$ in the following blanks spaces:
9 ...... A.
View full solution →If A = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} then insert the appropriate symbol $\in$ or $\not\in$ in the following blanks spaces:
-2 ...... A.
View full solution →If A = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} then insert the appropriate symbol $\in$ or $\not\in$ in the following blanks spaces:
4 ...... A.
View full solution →If A = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} then insert the appropriate symbol $\in$ or $\not\in$ in the following blanks spaces:
12 ...... A.
View full solution →