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

Q6   If $A \times B$  = {(a, x),(a , y), (b, x), (b, y)}. Find A and B.

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It is given that
$A \times B$  = {(a, x),(a , y), (b, x), (b, y)}
We know that the cartesian product of two non-empty set P and Q is defined as

$P \times Q = \left \{ (p,q) : p \ \epsilon \ P , q \ \epsilon \ Q \right \}$
Now, we know that A is the set of all first elements and B is the set of all second elements
Therefore,
$A= \left \{ a,b \right \} \ \ \ and \ \ \ B = \left \{ x , y \right \}$

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