1. The problem statement, all variables and given/known data Prove the absorption law A U (A and B) = A 2. Relevant equations 3. The attempt at a solution I need to prove the sets are equal. I don't know how to prove the right hand as a subset of the left hand. For left hand as subset of right hand, it's pretty simple (we can define a new called G holding x in A and in B), and G is subset of A, then G U A is A (definition of subset and Union). But how do I prove the right hand? I started writing "There exists a set A...." and I thought about using partition, but then I couldn't go on anymore. If I say there exists an arbitrary set B, and x in A and B, then I am again writing the first proof. Can someone please help me? Thanks.