If U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10},
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)’=_____

Solution:

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)’ = (⋂ A‘)’

 = C‘ ∪ A

= {1, 5, 6, 7, 9, 10} ∪ {1, 2, 3, 5}

(C – A)’ = {1, 2, 3, 5, 6, 7, 9, 10}

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