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Question

If A = {x : x = 2n, n ϵ W and n < 4}, B = {x: x = 2 n, n ϵ N and n 4} and C = {0, 1, 2, 5, 6}, then verify the associative property of intersection of sets. [5 marks]

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Solution

A = {x : x = x=2n, n ϵ W, n < 4}

x=20=2

x=21=2

x=22=4

x=23=8

A={1,2,4,8} [1 mark]

B = {x : x = 2n, n ϵ N and n 4}

x=2×1=2

x=2×2=4

x=2×3=6

x=2×4=8

B={2,4,6,8} [1 mark]

C = {0, 1, 2, 5, 6}

Associative property of intersection of sets

A (B C) = (A B) C

B C = {2, 6} [1 mark]

A (B C) = {1, 2, 4, 8} {2, 6} = {2} ...(1) [½ mark]

A B = {1, 2, 4, 8} {2, 4, 6, 8} = {2, 4, 8} [1 mark]

(A B) C = {2, 4, 8} {0, 1, 2, 5, 6} = {2}... (2) [½ mark]

From (1) and (2), It is verified that A (B C) = (A B) C

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