Question

Let A and B be two non empty sets such that $n\left(A\right)=5,n\left(B\right)=6$ and $n(A\cap B)=3$.

Find (i) $n(A\times B)$,

(ii) $n(B\times A)$ and

(iii) $n(A\times B)\cap (B\times A)$

Answer 1

(i) $n(A\times B)=n\left(A\right)\times n\left(B\right)=(5\times 6)=30$

(ii) $n(B\times A)=n\left(B\right)\times n\left(A\right)=(6\times 5)=30$

(iii) Given: $n(A\cap B)=3$

$\therefore$ A and B have 3 elements in common.

So, $(A\times B)$ and $(B\times A)$ have $3^2=9$ elements in common.

Hence, $n(A\times B)\cap (B\times A)=9$