Question

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

Answer 1

Given:
$A\times B=$ {$(a,x),(a,y),(b,x),(b,y)$}

Compare $A\times B$ and {$(a,x),(a,y),(b,x),(b,y)$}
We know that the cartesian product of two non-empty sets $P$ and $Q$ is given by : $P\times Q=$ {$(p,q):pϵP,qϵQ$}
Hence, $A$ is set of all first elements and $B$ is the set of all second elements.
$A=$ {$a,b$}, $B=$ {$x,y$}