The statement $p\to q\leftrightarrow\neg q\to\neg p$ is the equivalence between a conditional and its contrapositive. Since a conditional and its contrapositive are logically equivalent, this biconditional is always TRUE — it is a tautology. $p\wedge\neg p$ is a contradiction; $p\to\neg q$ is not always true; $(p\to q)\cap(p\wedge q)$ can be false.