1. The problem statement, all variables and given/known data The problem is to prove that there is only one empty set. Let A and B be empty sets, A is a subset of B and B is a subset of A (by the definition that the empty set is a subset of every set) So A=B (by definition) By convention, all empty sets are equal. Therefore, there is only one empty set. I'm fine with everything except the last line. I don't know if its my wording but something just doesn't feel right about it.