Question

If U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A = {1, 2, 3, 5), B = {2, 4, 6, 7) and C = {2, 3, 4, 8}. Then, ____________.
(i) (B ∪ C)'=_____
(ii) (C – A)'=_____

Answer 1

If U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
A = {1, 2, 3, 5), B = {2, 4, 6, 7) and C = {2, 3, 4, 8}
A' = {4, 6, 7, 8, 9, 10}, B' = (1, 3, 5, 8, 9, 10) and C' ={1, 5, 6, 7, 9, 10}
Then (B ∪ C)' = B' ⋂ C'
= {1, 3, 5, 8, 9, 10} ⋂ {1, 5, 6, 7, 9, 10}
i.e (B ∪ C)' = {1, 5, 9, 10} and (C – A)' = (C ⋂ A')'
= C' ∪ A
= {1, 5, 6, 7, 9, 10} ∪ {1, 2, 3, 5}
(C – A)' = {1, 2, 3, 5, 6, 7, 9, 10}