# Practice Test on Venn Diagrams

Practice test on Venn diagrams will help to test your knowledge on sets and Venn diagrams. After practicing the sets and Venn diagrams worksheets, this practice test on Venn diagrams are great for testing students on set theory and working with Venn diagrams.

1. From the adjoining figure list the elements of the following sets:

(a) ξ

(b) A'

(c) B'

(d) (A ∩ B)'

(e) (A ∪ B)'

(f) A' ∪ B'

2. Let A = {1, 2, 3, 5, 6}, B = {3, 4, 6, 8} be two subsets of the universal set ξ = {1, 2, 3, 4, 5, 6, 7, 8}

Draw Venn diagrams to represent the following sets:

(a) A'

(b) B'

(c) A ∪ B

(d) A ∩ B

(e) (A ∪ B)'

(f) (A ∩ B)'

More problems on practice test on Venn diagrams
3. Use the adjacent Venn diagram to find

(a) A

(b) B

(c) A'

(d) B'

(e) A - B

(f) B - A

(g) (A - B)'

(h) (B - A)'

4. Use Venn diagram to show (A ∩ B)’ = A’∪B’

to show A ∩ B when BCA

to show A ∪ B when BCA

5. What do the shaded regions in the following represent?

6. Use the adjoining figure to find the following sets:

(a) A ∪ B

(b) B ∩ C

(c) C - A

(d) A - B

(e) (B - C) ∪ A

(f) (C ∩ B) ∪ A

(g) (A ∪ B) ∩ C

(h) (B ∪ C)'

(i) (A ∪ B) - C

(j) (B - A)'

Word Problems on Practice Test on Venn Diagrams:

7. If A and B are two sets such that A ∪ B has 60 elements. A has 32 elements and B has 40 elements. How many elements does A ∩ B have?

8. If X and Y are two sets such that X has 30 elements and X ∪ Y has 50 elements and X ∩ Y has 8 elements, how many elements does Y have?

9. Find n(A ∪ B) if n(A) = 43, n(B) = 51 and n(A ∩ B) = 30.

10. In a class, 60% students like math whereas 50% like science. What per cent of students like both math and science?

11. There are 100 teachers in a school. 60 teach science, 25 teach humanities, 15 teach both science and humanities.

Find the number of teachers who teach:

(a) science but not humanities.

(b) Humanities but not science.

(c) Humanities or science.

12. In a group, 25 persons like tea or coffee, of these 15 like tea and 6 like both coffee and tea. How many like coffee?

13. In a survey of 40 students in a class, 10 were fond of having pineapple juice, 15 were fond of orange juice and 7 liked to have both pineapple as well as orange juice. Find how many students were taking neither pineapple juice nor orange juice.

14. In a survey, Sam found that 38 people liked product A, 36 liked product B, and 39 liked product C. If 24 people liked both products A and B, 20 people liked products C and A, 18 people liked product B and C, and 9 liked all the three products. Find how many liked product C only?

15. In a group of 60 students, 25 play table tennis, 16 do swimming and 22 play cricket, 8 play table tennis and do swimming, 6 play cricket and do swimming, 5 play table tennis and cricket, and 12 students do not play any of these game.

Find:

(a) how many play table tennis, do swimming and play cricket?

(b) How many play table tennis but not cricket?

(c) How many play table tennis and cricket but not do swimming?

Answers for practice test on Venn diagrams are given below to check the exact answer.

1. (a) {a, b, c, d, e, f, g, h, i, j}
(b) {d, e, f, g, h, i, j}
(c) {a, b, g, h, i, j}
(d) {a, b, d, e, f, g, h, i, j}
(e) {g, h, i, j}
(f) {a, b, d, e, f, g, h, i, j}

2.

A’ = {4, 7, 8}

B’ = {1, 2, 5, 7}

A ∪ B = {1, 2, 3, 4, 5, 6, 8}

A ∩ B = {3, 6}

(A ∪ B)’ = {7}

(A ∩ B)’ = {1, 2, 4, 5, 7, 8}

3. (a) {c, d, e, f, g, h, i}
(b) {e, f, i}
(c) {a, b, j}
(d) {a, b, c, d, g, h, j}
(e) {c, d, g, h}
(f) ∅
(g) {a, b, e, f, i, j}
(h) {a, b, c, d, e, f, g, h, i, j}

4.

(A ∩ B)’ = A’ ∪ B’

A ∩ B = B

A ∪ B = A

5. (a) B - A
(b) A ∪ B
(c) A - B
(d) (A ∩ B) ∪ (B ∩ C)
(e) B – A = ∅
(f) A ∩ B = ∅
(g) A ∩ B
(h) A ∩ B
(i) A ∩ B ∩ C

6. (a) {a, b, c, d, j, k}
(b) ∅
(c) {h, i, q}
(d) {a, b, c}
(e) {a, b, c, d, j, k}
(f) {a, b, c, d}
(g) ∅
(h) {a, b, c, p, l, m, n}
(i) {a, b, c, d, j, k}
(j) {a, b, c, d, h, i, p, q, l, m, n}

7. 12

8. 28

9. 64

10. 10%

11. (a) 45
(b) 10
(c) 70

12. 16

13. 22

14. 10

15. (a) 4
(b) 20
(c) 1

Set Theory

Sets