If the universal set $U = {1, 2, 3, 4, 5, 6, 7}, A = {1, 2, 5, 7}, B = {3, 4, 5, 6}$ . Verify ${(A \cup B)}^{'} = A^{'} \cap B^{'}$

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Solution

Given, universal set, $U = {1, 2, 3, 4, 5, 6, 7}$
$A = {1, 2, 5, 7}$
$B = {3, 4, 5, 6}$
$(A \cup B)^{'} = U - (A \cup B)$
$= {1, 2, 3, 4, 5, 6, 7} - {1, 2, 3, 4, 5, 6, 7}$
$= ϕ$
$A^{'} \cap B^{'} = (U - A) n (U - B)$
$= {3, 4, 6} n {1, 2, 7}$
$= ϕ$
Hence $(A \cup B)^{'} = A^{'} \cap B^{'}$ .

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