Question

If $A\times B=\left\{\right(a,x),(a,y),(b,x),(b,y\left)\right\}$ Find $A$ and $B$.

Answer 1

It is given that $A\times B=\left\{\right(a,x),(a,y),(b,x),(b,y\left)\right\}$
We know that the Cartesian product of two non-empty sets P and Q is defined as

$P\times Q=\left\{\right(p,q):p\in P,q\in Q\}$
$\therefore$ $A$ is the set of all first elements of $A\times B$ and $B$ is the set of all second elements of $A\times B$
Thus $A=\{a,b\}$ and $B=\{x,y\}$