Q:

Logical validity in first order logic

I'm having a problem understanding something.
In an excercise the following statement is wrong and I'm having trouble understanding why.
"If $a$ and $b$ are propositions then $(a \lor b)$ is valid if $a$ is valid or $b$ is valid."
Why is it wrong? Is there some interpretation where this doesn't hold?
Sorry if this is trivial, but I'm new to logic and I am trying to understand things

A:

It is true that $a \lor b$ is valid  (i.e., holds in all interpretations)  if either $a$ is valid or $b$ is valid. So, for example, $x^2 \ge 0 \lor x ^2 < 0$ is valid over the integers because $x^2 \ge 0$ is. The converse is not true: $a \lor b$ may be valid when neither $a$ nor $b$ on its own is valid, because $b$ may hold in the interpretations where $a$ does not.   E.g., over the integers $x \le 0 \lor x > 0$ is valid, while neither $x\le 0$ nor $x > 0$ is valid.

