Proof Writing & Problem Solving · Challenge problem

A two-input truth function assigns a truth value to "$P \diamond Q$" for each of the four combinations of truth values of $P$ and $Q$, so there are $16$ such functions ("if … then", "and", "or", …). Call $\diamond$ contrapositive-proof if "$P \diamond Q$" always has the same truth value as "$(\text{not } Q) \diamond (\text{not } P)$". How many of the $16$ functions are contrapositive-proof?