Question

Given a conditional statement p → q, which statement is logically equivalent?

~p → ~q
~q → ~p
q → p
p → ~q

Answer 1

~q → ~p

This is the contrapositive of p → q and is always logically equivalent. Briefly: if p → q and ~q holds, p cannot hold (otherwise q would), so ~p; and conversely taking the contrapositive of ~q → ~p returns p → q.