Question

Let $A=\{1,4,7,10,13,16,19\},$ $B=\{1,2,3,4,5,6\},$ $C=\{2,8,14,20\},$ then $n[A\times (B^{\prime }\cap C^{\prime }{)}^{\prime }]=$

Answer 1

$A=\{1,4,7,10,13,16,19\}\Rightarrow n\left(A\right)=7$
$B=\{1,2,3,4,5,6\}$
$C=\{2,8,14,20\}$

$A\times (B^{\prime }\cap C^{\prime }{)}^{\prime }=A\times ((B\cup C{)}^{\prime }{)}^{\prime }=A\times (B\cup C)B\cup C=\{1,2,3,4,5,6,8,14,20\}$
$n(B\cup C)=9$

$n[A\times (B^{\prime }\cap C^{\prime }{)}^{\prime }]=n[A\times (B\cup C)]=n(A)\times n(B\cup C)=7\times 9=63$