Scope of quantifiers

$P_1$. $\forall x,\ P(x)\Rightarrow Q$: if all $x$ satisfy $P$, then $Q$. Here $Q$ does not depend on $x$; the quantifier applies only to $P(x)$.

$P_2$. $\forall x,\ (P(x)\Rightarrow Q)$: for every $x$, if $P(x)$ then $Q$. Each implication is quantified separately.

Example. $P(x)$: "$x$ is a counterexample"; $Q$: "the conjecture is false". $P_1$: "if all are counterexamples, the conjecture is false". $P_2$: "every counterexample makes the conjecture false".

Conclusion. Scope matters: $\forall x,\ P(x)\Rightarrow Q$ and $\forall x,\ (P(x)\Rightarrow Q)$ differ in meaning.