I'd like to ask a very simple question. Why do we use "vel" between the solutions of inequalities?
I mean, to solve
$ \ \ \large x^2-7x \geq 0$ we write $\large x\leq 0 \vee x \geq 7 $.
Aren't we supposing that there's a possibility to have contemporarely two $x$ values using the logical OR?
Shouldn't we be using the logical XOR (also known as $\bigoplus$)?
$$\large x\leq 0 \ \scriptsize \bigoplus \ \ \large x \geq 7 $$
$x$ can obviously be only either in one range or the other, why are we considering that it can belong to both? Thanks for your time in advance.
Here $\vee$ means "or". But (as you noted) it is confusing. So just write "or" instead. Even worse is $\oplus$ for exclusive or. Do not use it in mathematical writing. In words you can say " ... or ... but not both". That will make it clear to the reader [the purpose of mathematical writing is to make it clear to the reader].
In this case, $x$ cannot satisfy both. So you could write "$x \le 0$ or $x \ge 7$ but not both". Of course this is the same as "$x \le 0$ or $x \ge 7$", so you could write that (as your source did). If both is impossible, then there is no need to assert "but not both" unless you want to for fun.