Question

If $n\left(A\right)=m$ and $n\left(B\right)=n$ ; then $n(A\times B)=mn$.

What is the value of $n(A\times B)=mn$. if $m=6$ and $n=8$

Answer 1

Cartesian product of two sets is obtained by pairing each element of first set with each element of second set.
Given : $n\left(A\right)=m$ and $n\left(B\right)=n$
Now, $n(A\times B)=n\left(A\right)\times n\left(B\right)=m\times n=mn$.

Thus when $m=8$ and $n=6$, we have $n(A\times B)=48$