If A = {x : x ϵ N, x ≤ 7}, B = {x : x is prime, x

Question

If A = {x : x ϵ N, x ≤ 7}, B = {x : x is prime, x < 8} and C = {x : x ϵ N, x is odd and x < 10}, verify that:
(i) A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C)

(ii) A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C)

Philoid · Accepted Answer

Natural numbers start from 1

A = {1, 2, 3, 4, 5, 6, 7}

B = {2, 3, 5, 7}

C = {1, 3, 5, 7, 9}

(i) BC = {3, 5, 7}
AU(BC) = {1, 2, 3, 4, 5, 6, 7}

AB = {1, 2, 3, 4, 5, 6, 7}

AC = {1, 2, 3, 4, 5, 6, 7, 9}

(AB)(AC) = {1, 23, 4, 5, 6, 7}

A(BC) = (AB)(AC)

Hence proved

(ii) BC = {1, 2, 3, 5, 7, 9}

A(BC) = {1, 2, 3, 5, 7}

AB = {2, 3, 5, 7}

AC = {1, 3, 5, 7}

(AB)(AC) = {1, 2, 3, 5, 7}

A(BC) = (AB)(AC)

Hence proved