If $U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}$ , $A = {0, 3, 4, 7}$ , $B = {1, 2, 8, 9}$
then $(A U B)^{'}$ is

{2, 5}

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{5, 6}

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{8, 9}

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{6, 7}

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Solution

The correct option is D ${5, 6}$
Given, $U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}$ , $A = {0, 3, 4, 7}$ , $B = {1, 2, 8, 9}$

$A^{c} = {1, 2, 5, 6, 8, 9}, B^{c} = {0, 3, 4, 5, 6, 7}$

By De Morgan's law

$(A \cup B)^{c} = A^{c} \cap B^{c}$

$= {1, 2, 5, 6, 8, 9} \cap {0, 3, 4, 5, 6, 7}$

$= {5, 6}$

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