Old Dominion University: Shunichi Toida's "Properties of Set Operation"

Read this page. It is important that you become aware that sets combine under union and intersection in very much the same ways that numbers combine under addition and multiplication. For example,  A\cup B=B\cup A is a way to say union is commutative in the same way as   x + y = y + x says addition is commutative. One difference, however, is that the properties of addition and multiplication are defined as part of the number system (in our development) whereas the properties of sets under the operations we have defined are provable and hence must be proved.