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