# Parentheses and quantifiers [closed]

What is the difference between
$$\forall x,\exists y, ((x,y) \in A \implies x \in B)$$ and $$\forall x,((\exists y, (x,y) \in A) \implies x \in B)$$ ?

I understand that the second means that $$pr_1 A \subseteq B$$, but what about the first sentence ?

## closed as off-topic by Yemon Choi, Andreas Blass, Emil Jeřábek, Alexey Ustinov, Matt F.Sep 11 at 14:27

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "MathOverflow is for mathematicians to ask each other questions about their research. See Math.StackExchange to ask general questions in mathematics." – Yemon Choi, Andreas Blass, Emil Jeřábek, Alexey Ustinov
If this question can be reworded to fit the rules in the help center, please edit the question.

• The first sentence is equivalent to $\forall x\,((\forall y\,(x,y)\in A)\implies x\in B)$. – Andreas Blass Sep 11 at 14:18