# Practice Test on Operations on Sets

In practice test on operations on sets we will solve 8 different types of questions on more about sets. The questions will be mainly related to union of sets, intersection of sets and difference of sets.

Practice Test on Operations on Sets

1. If A = {2, 3, 4, 5}     B = {4, 5, 6, 7}     C = {6, 7, 8, 9}     D = {8, 9, 10, 11}, find

(a) A ∪ B

(b) A ∪ C

(c) B ∪ C

(d) B ∪ D

(e) (A ∪ B) ∪ C

(f) A ∪ (B ∪ C)

(g) B ∪ (C ∪ D)

2. If A = {4, 6, 8, 10, 12} B = {8, 10, 12, 14} C = {12, 14, 16} D = {16, 18}, find

(a) A ∩ B

(b) B ∩ C

(c) A ∩ (C ∩ D)

(d) A ∩ C

(e) B ∩ D

(f)(A ∩ B) ∪ C

(g) A ∩ (B ∪ D)

(h) (A ∩ B) ∪ (B ∩ C)

(i) (A ∪ D) ∩ (B ∪ C)

3. If A = {4, 7, 10, 13, 16, 19, 22}   B = {5, 9, 13, 17, 20}
C = {3, 5, 7, 9, 11, 13, 15, 17}   D = {6, 11, 16, 21} then find

(a) A - C

(b) D - A

(c) D - B

(d) A - D

(e) B - C

(f) C - D

(g) B - A

(h) B - D

(i) D - C

(j) A - B

(k) C - B

(l) C - A

More Practice Test on Operations on Sets
4. If A and B are two sets such that A ⊂ B, then what is A∪B?

5. Find the union, intersection and the difference (A - B) of the following pairs of sets.

(a) A = The set of all letters of the word FEAST

B = The set of all letters of the word TASTE

(b) A = {x : x ∈ W, 0 < x ≤ 7}

B = {x : x ∈ W, 4 < x < 9}

(c) A = {x | x ∈ N, x is a factor of 12}

B = {x | x ∈ N, x is a multiple of 2, x < 12}

(d) A = The set of all even numbers less than 12

B = The set of all odd numbers less than 11

(e) A = {x : x ∈ I, -2 < x < 2}

B = {x : x ∈ I, -1 < x < 4}

(f) A = {a, l, m, n, p}

B = {q, r, l, a, s, n}

6. Let X = {2, 4, 5, 6}   Y = {3, 4, 7, 8}   Z = {5, 6, 7, 8}, find

(a) (X - Y) ∪ (Y - X)

(b) (X - Y) ∩ (Y - X)

(c) (Y - Z) ∪ (Z - Y)

(d) (Y - Z) ∩ (Z - Y)

Practice Test on Operations on Sets

7. Let ξ = {1, 2, 3, 4, 5, 6, 7} and A = {1, 2, 3, 4, 5} B = {2, 5, 7} show that

(a) (A ∪ B)' = A' ∩ B'

(b) (A ∩ B)' = A' ∪ B'

(c) (A ∩ B) = B ∩ A

(d) (A ∪ B) = B ∪ A

8. Let P = {a, b, c, d}   Q = {b, d, f}   R = {a, c, e} verify that

(a) (P ∪ Q) ∪ R = P ∪ (Q ∪ R)

(b) (P ∩ Q) ∩ R = P ∩ (Q ∩ R)

Answers for practice test on operations on sets are given below to check the correct answers.

1. (a) {2, 3, 4, 5, 6, 7}
(b) {2, 3, 4, 5, 6, 7, 8, 9}
(c) {4, 5, 6, 7, 8, 9}
(d) {4, 5, 6, 7, 8, 9, 10, 11}
(e) {2, 3, 4, 5, 6, 7, 8, 9}
(f) {2, 3, 4, 5, 6, 7, 8, 9}
(g) {4, 5, 6, 7, 8, 9, 10, 11}

2. (a) {8, 10, 12}
(b) {12, 14}
(c) ∅
(d) {12}
(e) d
(f) {8, 10, 12, 14, 16}
(g) {8}
(h) {8, 10, 12, 14}
(i) {8, 10, 12, 16}

3. (a) {4, 10, 16, 19, 22}
(b) {6, 11, 21}
(c) {6, 11, 16, 21}
(d) {4, 7, 10, 13, 19, 22}
(e) {20}
(f) {3, 5, 7, 9, 13, 15, 17}
(g) {5, 19, 17, 20}
(h) {5, 9, 13, 17, 20}
(i) {6, 16, 21}
(j) {4, 7, 10, 16, 19, 22}
(k) {3, 7, 11, 15}
(l) {3, 5, 9 11, 15, 17}

4. B

5. (a) {F, E, A, S, T}, {E, A, S, T}, {F}
(b) {1, 2, 3, 4, 5, 6, 7, 8}, {5, 6, 7}, {1, 2, 3, 4}
(c) {1, 2, 3, 4, 6, 8, 10, 12}, {2, 4, 6}, {1, 3, 12}
(d) {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, d, {2, 4, 6, 8, 10}
(e) {-1, 0, 1, 2, 3}, {0, 1}, {-1}
(f) {a, 1, m, n, p, q, r, s}, {a, l, n}, {m, p}

6. (a) {2, 3, 5, 6, 7, 8}
(b) d
(c) d {3, 4, 5, 6}
(d) d

7. (a) L.H.S. = R. H. S = {6}
(b) L.H.S. = R. H. S = {1, 3, 4, 6, 7}
(c) {2, 5}
(d) {1, 2, 3, 4, 5, 7}

8. (a) {a, b, c, d, e, f}
(b) d

Set Theory

Sets