/sci/ - Science & Math

I am getting filtered by fucking propositional logic.
does p then q necessarily imply that if not p then not q?
are the the statements "p if q" and "p only if q" equal?
my intuition says the first implies p being false doesn't imply q is false while the latter implies it.
is it just semantics? can both be written as [math]p \to q[/math] ?