The product of xy of two real numbers x and y is irrational then at least one of the x or y must be irrational.

Question

Prove if true or find a counterexample....

The product of $x y $ of two real numbers $x$ and $y$ is irrational then at least one of the $x$ or $y$ must be irrational.

Answer 1

Assume that $x$ and $y$ are rationals, then so is $xy$. That's the contrapositive of your proposition!