1. The problem statement, all variables and given/known data We have an equivalence relation such that A <-> B. Prove that the equivalence relation is true. 3. The attempt at a solution Let P: A -> B Q: B -> A Let's prove the relation by contradiction. Assume [tex]\neg A -> \neg B [/tex] The previous assumption is the same as Q. Thus, we have a contradiction, since it is impossible that both of the following Q and [tex] \neg Q[/tex] are true at the same time, where Q: B -> A and [tex]\neg Q: \neg A -> \neg B [/tex] which is the same as B -> A. Thus, the equivalence relation is true between A and B.