## camelialawson How do I Prove or disprove; For all x, y € R, if x is rational and y is irrational, then xy is irrational 2 years ago 2 years ago

$$x$$ is rational, so $$x$$ can be expressed as $$\frac{p}{q}$$ Let us assume that $$x\times y$$ is rational, then $$xy=\frac{m}{n}\implies y=\frac{mq}{np}$$ . This shows that y is rational, which is a contradiction. So $$xy$$ is irrational.