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$.