Question

If A and B have n elements in common,then the number of elements common to $A\times BandB\times A$ is:

Answer 1

Let A and B be two non-empty sets heaving n elements in common, then we have

$(A\times B)\cap (C\times D)=(A\cap C)\times (B\cap D)$

It is given that $n(A\cap B)=n$ elements

Now $n\left[\right(A\cap B)\times (B\cap A\left)\right]=n.n=n^2$ elements

Hence, $A\times B$ and $B\times A$ have $n^2$ elements in common .