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