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

Question

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Answer 1

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 sets P and Q is defined as
$P \times Q = {(p, q) : p \in P, q \in Q}$
$∴$ $A$ is the set of all first elements of $A \times B$ and $B$ is the set of all second elements of $A \times B$
Thus $A = {a, b}$ and $B = {x, y}$

Answer 2

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 sets P and Q is defined as

P \times Q = {(p, q) : p \in P, q \in Q}

∴

A

is the set of all first elements of

A \times B

and

B

is the set of all second elements of

A \times B

Thus

A = {a, b}

and

B = {x, y}