Question

If A and B are two sets having 3 elements in common. If n(A) = 5 and n(B) = 4, find $n\left[\right(A\times B)$ and $n(A\times B)\cap (B\times A)]$.

Answer 1

We have,

n(A) = 5 and n(B) = 4

We know that, if A and B are two finite sets, then $n(A\times B)=n\left(A\right)\times n\left(B\right)$

$\therefore n(A\times B)=5\times =20$

Now,

$n\left[\right(A\times B)\cap (B\times A\left)\right]=3\times 3=9$

[$\because$ A and B have 3 elements in common]