Question

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

Find A and B. 

Answer 1

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 and B is the set of all second elements. 

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