Question

Suppose that the number of elements in set $A$ is $p$, the number of elements in set $B$ is $q$ and the number of elements in $A\times B$ is $7$. Then $p^2+q^2=$

• A. $42$
• B. $49$
• C. $50$
• D. $51$

Answer 1

Answer: (C)

$n(A)=p$,
$n(B)=q$,
$n(A\times B)=pq=7$
So possible values of $p$, $q$ are $7$, $1$
$\Rightarrow p^2+q^2$
$=(7{)}^2+(1{)}^2=50$.