Chapter 3: Extra Exercise

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. 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



4. 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) 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}


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