## anonymous 4 years ago How do I Prove or disprove; For all x, y € R, if x is rational and y is irrational, then xy is irrational

1. 2bornot2b

$$x$$ 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.

2. 2bornot2b

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