Question

If A×B={(a,x),(a,y),(b,x),(b,y)}. Find A and B

Answer 1

A×B={(a,x),(a,y),(b,x),(b,y)}
We know that,
If P and Q are any two sets then,
P×Q={(p,q):p belongs to P , q belongs to Q}

Applying this concept we get,
A={a,a,b,b}
A={a,b}
and
B={x,y,x,y}
B={x,y}
Here corresponding first elements belong to A and corresponding second elements belong to B.

Hence,
A={a,b} and
B={x,y}

Answer 2

A X B = { (a,x), (a,y) , (b,x), (b,y) }

if A and B are two sets
AXB = { (a,b) / a∈A and b∈B}
from above definition

A = {a, b}
B = {x,y}