Part 1

Attempt all questions

1

Given that A = {3, 5, 7,9}, B = {2,4,6,8}

and C = {x: 3 < x < 9} are subsets of a

universal set, u = {2, 3, 4, 5, 6, 7, 8, 9}.

Find:

a) An (B'n C')

b) (AUB) n (BUC)

a) A n (B' n C') = {3, 9}.

b) (AUB) n (BUC) = {2,4,5,6,7,8}

Step-by-step explanation:

a) Rewriting C; C = {4,5,6,7,8}

B' = {3,5,7,9} and C' = {2, 3, 9}

so (B' n C') = {3, 9}

and A n (B' n C') = {3, 9}.

b) {A U B} = { 2,3,4,5,6,7,8,9} and {B U C} = {2,4,5,6,7,8}

so (AUB) n (BUC) = {2,4,5,6,7,8}