algebra precalculus - What does the notation in this claim, that needs to be proved, mean?

Prove, or disprove using a counter example:

Let $p,q\in\mathbb{R}$ \ $\mathbb{Q}$ \, then $p-q$ is irrational.

I don't understand what the back slash between the $\mathbb{R}$ and $\mathbb{Q}$ means.

Answer

The $\setminus$ sign means substraction of sets.

$$A\setminus B = \{x\in A \mbox{ such that } x\not\in B\}.$$

In your case, $\mathbb{R}\setminus\mathbb{Q}$ is the set of irrational numbers.