I realise that Math SE $\neq$ Philosophy SE, but what questions of logic can be posed? Particularly, can any question of logic involving symbols be asked here? (This is what I mean by 'symbolic logic' in the question title; please advise if I've erred).
Logic in Philosophy vs. Mathematical Logic inspired this question. I'm unversed in logic or philosophy, but am confused by the allowance of
1. Logic nonsense/paradox,
2. Why is predicate "all" as in all(SET) true if the SET is empty?,
3. Why is this true? $(\exists x)(P(x) \Rightarrow (\forall y) P(y))$,
4. Implies vs. Entails vs. Provable,
5. In classical logic, why is $(p\Rightarrow q)$ True if both $p$ and $q$ are False? ,
contrary to the closures of the following, NOT by reason of being duplicates: