Question

Let U = {1, 2, 3, 4, 5, 6, 7}, A = {2, 4, 6}, B = {3, 5} and C = {1, 2, 4, 7}, find
(i) A′ ∪ (B ∩ C′)
(ii) (B – A) ∪ (A – C)

Answer 1

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

A = {2 , 4 , 6}

B = {3 , 5}

C = {1 , 2 , 4 , 7}

(i) A' ∪ (B ∩ C')

For this first we find

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

A' = {1 , 3 , 5 , 7}

C' = U - C = {1,2,3,4,5,6,7} - {1,2,4,7}

C' = {3, 5 , 6}

(B ∩ C') = {3 , 5} ∩ {3 , 5 , 6}

B ∩ C' = {3 , 5}

Now,

A' U (B ∩ C') = {1,3,5,7} U {3 , 5}

A' ∪ (B ∩ C') = {1 , 3 , 5 7}

(ii) (B - A) ∪ (A - C)

For this first we find

B - A = {3 , 5} - {2 , 4 , 6}

B - A = Φ

A - C = {2 , 4 , 6} - {1 , 2 , 4 , 7}

A - C = {6}

Now,

(B - A) ∪ (A - C) = Φ ∪ {6}

(B - A) ∪ (A - C) = {6}