Question 3 12 marks Let A a b c B 1 2 3 and C a 2 Determi

Question 3 (12 marks) Let A = {a, b, c}, B = {1, 2, 3} and C = {a, 2}. Determine each of the

Following sets (i.e., write in the form of S = {, , , ...}).

(1) C (A B), (ii) (C A) B, (iii) A × C, (iv) C × A, (v) P(B).

(2). given any three sets A, B and C, prove (without using Venn diagram) that

A (B C) = (A B) (A C)

Given that A = {a, b, c}, B = {1, 2, 3} and C = {a, 2}

1) i) C (A B) = {a,2} {a, b, c,1, 2, 3} = {a,2}

ii) (C A) B = {a} {1,2,3} = {a,1,2,3}

iii) A × C = { (a,a), (a,2), (b,a),(b,2), (c,a), (c,2) }

(iv) C × A = { (a,a), (2,a), (a,b),(2,b ), (a,c), (2,c) }

2) A (B C) = (A B) (A C)

A (B C) = {a,b,c}- { 1,2,3,a} = {b,c}

(A B) (A C) = {a,b,c} { b,c} = {b,c}

Therefore,

A (B C) = (A B) (A C)