1. The problem statement, all variables and given/known data Prove that if A=B if and only if [itex] A \subseteq B [/itex] and [itex] B \subseteq A [/itex] 3. The attempt at a solution If A is a subset of B then all the elements of A are in B . And if B is a subset of A then all the elements of B are in A . There fore there is a one-to-one correspondence between the 2 sets therefore they are equal. Is this to simple or do I need to be more rigorous.