If $x\in\mathbb{R}$ and $y\in\mathbb{R}$ then $\frac xy\in\mathbb{R}$?

Question

Check whether the following statement is true or not:

If $x\in\mathbb{R}$ and $y\in\mathbb{R}$ then $\frac xy\in\mathbb{R}$

For $y\neq0$ I think the statement is true. But when $y=0$ we have a number divided by zero and it is undefined hence it is not a real number. So I think the statement is not true. Am I right?

Answer 1

You are correct. The statement should be $$x \in \mathbb{R} \land y \in \mathbb{R}^{\star} \implies \frac{x}{y} \in \mathbb{R}.$$