If A×B={(a,x),(a,y),(b,x),(b,y)} Find A and B.
It is given that A×B={(a,x),(a,y),(b,x),(b,y)}
We know that the Cartesian product of two non-empty sets P and Q is defined as
P×Q={(p,q):p∈P,q∈Q}
∴ A is the set of all first elements of A×B and B is the set of all second elements of A×B
Thus A={a,b} and B={x,y}