I'm sure this is a very simple question, but I cannot manage to find it explictly answered anywhere. Do parentheses used for quantifiers also affect logical operators normally?
For example, if parentheses affect logical operators normally, the following formula:
$\forall x(P(x) \land \exists y(Q(y) \rightarrow R(x,y)))$
Would be equivalent, in terms of its structure, to:
$P \land (Q \rightarrow R)$
Whereas this one:
$\forall x(P(x) \land \exists y(Q(y)) \rightarrow R(x,y))$
Would be equivalent to:
$P \land Q \rightarrow R \equiv (P \land Q) \rightarrow R$
If it turns out that parentheses used for quantifiers do not affect the preference of "non-quantifier" logical operators, then both cases would be the same... So could someone please confirm whether I am right, and parentheses used for quantifiers affect all logical operators normally?
Thanks in advance for your time! :)