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

Given: A × B = {(a, x), (a, y), (b, x), (b, y)}

By definition of Cartesian product of two non-empty Set P and Q:

P × Q = {(p, q): p Є P, q Є Q}

Hence, we see A = set of all first elements.

B = set of all second elements.

⇒ A = {a,b} and B = {x,y}.