Question

If U = {1, 2, 3, 4, 5,6,7,8, 9},

A = {2, 4, 6, 8} and B = {2, 3, 5, 7}. 

Verify that

(i) (AUB)'= A'∩B'

(ii) (A∩B)'=A'UB'

Answer 1

U = {1, 2, 3, 4, 5, 6, 7, 8, 9}

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

(i) (AUB)' = {2,3,4,5,6,7,8}' = {1,9}

A'∩B' = {1,3,5,7,9}∩{1,4,6,8,9} = {1,9}

∴ (AUB)'= A'∩B'

(ii) (A∩B)' = {2}' = {1,3,4,5,6,7,8,9}

A'UB' = {1,3,5,7,9}U{1,4,6,8,9}

={1,3,4,5,6,7,8,9}

(A∩B)'=A'UB'