**Venn Diagram Questions**, you can increase the understanding of the concepts learnt. These

**Venn Diagram Questions**are prepared by experienced teachers and subject matter experts.

**Read More About Union, Intersection and Venn Diagram**

**Venn
Diagram Questions with Answers**

**1.
**Choose the correct option.

a.
If *n*(A) = 6 and *n*(B) = 5, then maximum value of *n *(A ∪ B) is

i. 1

ii. 11

iii. 4

iv. 2

b.
If A ⊆ B and B ⊆ A, then A ∩ B =

i. A – B

ii. B – A

iii. a null set

iv.
A or B

c.
If Î¾ is the universal set and A ⊆ Î¾ with *n*(Î¾) = 100 and *n*(A) = 60, then *n*(A’)=

i. 60

ii. 80

iii. 40

iv. 50

**2. **Write true or false for each of the following
statements.

a. If A = {letters of the word BALLOON}, then n (A) = 5.

b. If P = {*x *: *x *∈ **W**, *x *is a multiple of 3
less than 15} and Q = {*x *: *x *∈ **N**, *x *is a multiple of 4
less than 15}, then P ∩ Q is a singleton set.

c. If set A and B are two equivalent
sets, then n (A) = n (B).

d. S = {students of class 8 in a
school} is a finite set.

**3.
**Fill in the blanks.

a.
If A = {*a*, *b*, *c, d, e, f*}, B = {letters of the word “fade”},
then A ∩ B is ___________.

b. If A = {letters of the word FLOWER}, then *n*(A)
is ___________.

c. If A = {letters of the word ARITHMETIC} and
B = {letters of the word TRIGONOMETRY}, then A ∩ B = ___________.

d. A = {5, 10, 15, 20, 25, 30}
written in set builder form is ___________.

**4. **Let Î¾ = {x: x Ñ” N and x < 13}, A = {2, 3, 5, 7, 11} and B = {2,
4, 6, 8, 10, 12}, find the following:

a. A′

b. A ∩ B

c. A ∪ B

d. B’

Draw
the Venn diagram for all operations in a to d.

**5. **In gathering of 50 diplomats, each person can
speak either English or French or both. If 36 speak English, 24 speak French,
how many speak both English and French? Solve this problem using a Venn
diagram.

**6. **In a group of 45 boys, each one play either
cricket or tennis. If 32 of them play cricket and 29 play tennis and 16 play
both, then represent this situation using Venn diagram.

**7. **If Î¾ = {x: x Ñ” N and 1 ≤ x ≤ 15}, A = {2, 3, 5, 7, 11, 13}, B =
{1, 2, 3, 4, 5, 6, 7} and C = {5, 6, 7, 8, 9, 10}. Find

a. B ∩ C

b. A ∪ B

c. A ∪ C

d. A ∪ (B ∩ C)

Verify that A ∪ (B
∩ C) = (A ∪ B) ∩ (A ∪ C)

**8.
**Given Î¾ = {1, 2, 3, 4, …, 25}. Write down the
elements of the following sets if A = {*x *: *x *Ñ”* *Î¾ and *x *is
odd} and B = {*x *: *x *Ñ” Î¾ and *x *is a multiple of 3}, find

a. the elements of A – B

b. A′

c. *n*(A∩B)

**9. **From the Venn diagram, find

a. A ∩ B

b. A ∪ B

c. A – B

d. B – A

e. (A ∪ B)’

**10. **Write down the sets represented by the shaded
portion in each of the following Venn diagrams.

**ANSWERS**

1. a. ii b. iv

c.
iii

2. a. True
b. True

c.
True d. True

3. a. {a, d, e, f} b. 6

c. {R,
I, T, M, E}

d. {x:
x = 5*n*; *n *∈
**N**; n < 7}

4. a. A′ = {1, 4, 6,
8, 9, 10, 12}

b. A ∩ B = {2}

c. A ∪
B = {2, 3, 4, 5, 6, 7, 8, 10, 11, 12}

d. B’ = {1, 3, 5, 7, 9, 11}

5. 10
persons

6. Do it
yourself

7. a. B ∩
C = {5, 6, 7}

b. A ∪
B = {1, 2, 3, 4, 5, 6, 7, 11, 13}

c. A ∪
C = {2, 3, 5, 6, 78, 9, 10, 11, 13}

d. A ∪
(B ∩ C) = {2, 3, 5, 6, 7, 11, 13}

8. a. A –
B = {1, 5, 7, 11, 13, 17, 19, 23, 25}

b. A′ = {2, 4, 6, 8, 10, 12, 14, 16, 18,
20, 22, 24}

c. *n*(A ∩ B) = 4

9. a. A ∩ B = {4}

b. A ∪ B = {1, 2, 3, 4, 5, 7, 8, 9}

c. A – B = {1, 2, 3, 8}

d. B – A = {5, 7, 9}

e. (A ∪ B)’ = {6, 10, 11, 12, 14, 18}

10. a. A – B

b. (A ∪
B)’

c. (A – B) ∪
(B – A)

d. A’

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