1. The problem statement, all variables and given/known data We say that two sets A and B have the "same powerfulness" if there is a bijection from A to B. Show that the relation "have the same powerfulness" is an equivalence relation between sets. 2. Relevant equations An equivalence relation satisfy the following: xRx (reflexive) xRy --> yRx (symmetric) xRy and yRz --> xRz (transitive) 3. The attempt at a solution I'm not sure on where to begin to show that they bijective functions are reflexive. They are symmetric since bijective functions can be reversed with the same domain (and same range). They are transitive since the function going from A --> B is surjective as well as injective, meaning that the the range of A is a perfect subset of B (the range of the function contains every value of B). So if we then have another function B --> C (regardless of the whether the function B --> C is injective or surjective??) then A --> C as well. So, I'm not sure how to show or rather explain that a bijective function is reflexive. And also, if my wording of why a bijective function is symmetric and transitive is wrong in any way, please correct me as I'm here to learn. Appreciate all the help. Thanks in advance!