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

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 $B=\{x, y\}$