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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.

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.

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