Question

Let U = {1,2,3,4,5,6}, A = {2,3} and B = {3,4,5}. Show that $(A\cup B{)}^{\prime }=A^{\prime }\cap B^{\prime }$.

Answer 1

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

A = {2,3}

B = {3,4,5}

$A\cup B=${2,3} $\cup$ {3,4,5} = {2,3,4,5}

Therefore, $(A\cup B{)}^{\prime }$ = {1,6}

Also, $A^{\prime }$ = {1,4,5,6}

$B^{\prime }$ = {1,2,6}

Therefore, $A^{\prime }\cap B^{\prime }$ = {1,4,5,6} $\cap$ {1,2,6} = {1,6}

Hence, $(A\cup B{)}^{\prime }=A^{\prime }\cap B^{\prime }$.