The contraposition equivalence is as follows:
So it may seem a small strange at first, this means that it appears which we have said nothing in the first sentence about ¬Q, than how can we infer anything from it in the second sentence? Moreover, suppose we know something that P implies Q, and we saw that Q was false. So there in this case, if we were to imply that P was true, so, is just that we know P implies Q and we also know that Q is true. If it so, Q was false! Thus we cannot possibly imply there that P is true, that means there we must imply that P is false because we are in propositional logic thus P must be either true or false. So we can say this argument shows there, we can replace the first sentence by the second one so it is left as an exercise to construct a similar argument for the vice-versa part of this similarity.