Question about correct notation

Question

Is the following way to define a set correct:

$\{A_p|A_p\in Z_2\&(\forall A_q \in Z_3)(A_p \cap A_q = 0)\}$

or is it better to write it this way:

$\{A_p|A_p\in Z_2\&(\forall A_q \in Z_3) A_p \cap A_q = 0\}$.

Answer 1

By convention, you don't need to put the brackets around the equation $A_p \cap A_q = 0$, because predicate symbols like $=$ are taken to have higher precedence than logical operators like $\&$ (because things like $x = (1 \mathrel{\&} a = b)$ are not well-formed in first-order logic, so there is only one meaningful way to read $x =1 \mathrel{\&} a = b$, namely as $(x = 1) \mathrel{\&} (a = b)$). It is not wrong to put the brackets in.