Why is predicate “all” as in all(SET) true if the SET is empty?
In don't quite understand this quantification over the empty set:
$\forall y \in \emptyset: Q(y)$
The book says that this is always TRUE regardless of the value of the predicate $Q(y)$, and it explain that this is because this quantification adds no predicate at all, and therefore can be considered the weakest predicate possible, which is TRUE.
I know that TRUE is the weakest predicate because $ $P$ \Rightarrow$ TRUE is TRUE for every $P$. I don't see what is the relationship between this weakest predicate and the quantification.