1. The problem statement, all variables and given/known data Let H and K be subgroups of the group G. Let a,b \in G and define a relation on G by a ~ b if and only if a = hbk for some h \in H and k \in K. Prove that this is an equivalence relation. 2. Relevant equations a = hbk 3. The attempt at a solution The goal is to prove the reflexive, symmetric, and transitive properties of equivalence. I was just hoping someone could help lead me in the right direction of how to start each one. Thanks!