Phrasing an instruction involving the "for all" quantifier

I did a number theory course where the instructor sometimes phrased an exercise in a way that seems slightly wrong. For example, he wrote the exercise

Check if the following statement is correct: for every positiveinteger $n$ we have that $q=p_1p_2\cdots p_n+1$ is prime where $p_n$ isthe $n$th prime.

as

For every positive integer $n$ let $q=p_1p_2\cdots p_n+1$ where $p_n$is the $n$th prime, check if the following statement is correct: "$q$is prime."

The way that he phrased the exercise is clear enough, but just seems weird, and I want to know if this style is common. I'm not asking for a solution to this problem, just whether this type of phrasing is normal?

More generally, can a question of the form "is it true that for every $x\in A$ we have $P(x)$?" be rephrased as "for every $x\in A$ is it true that $P(x)?$"?

Note: this is a question about mathematical writing, not about the logic of quantifiers.