Question

If A and B are two non-empty sets having n elements in common, then what is the number of common elements in the sets $A\times B$ and $B\times A$?

• A. $n$
• B. $n^2$
• C. $2n$
• D. Zero

Answer 1

Answer: (B)

$n^2$

Say A has x elements and B has y elements in total.

Their cartesian product $A\times B$ will have $x\times y$ elements.

Hence if they have n elements in common. $n^2$ common elements are present in the products $A\times B$ and $B\times A$