Question

IN Three marks questions:
11 If U = {1,2,3,4,5,6). A=(2.3), and B=(3,4,5) thea verify that (AUB) = A'UB'
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Answer 1

Solution:

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

A = {2, 3}

A’ = {1, 4, 5, 6}

B = {3, 4, 5}

B’ = {1, 2, 6}

A⋃B = {2, 3, 4, 5}

A’⋃B’ = {1, 2, 4, 5, 6}

Therefore, they are not equal.

But
(A⋃B)’ = A’⋂B’

A⋃B = {2, 3, 4, 5}

(A⋃B)’ = {1, 6}

A’⋂B’ = {1, 4, 5, 6} ⋂ {1, 2, 6} = {1, 6}

This is (A ⋃ B)' = A' ∩ B' (which is a De Morgan's law of union).

Hope this will be helpful.