If you (or your teacher) finds drawing Venn diagrams sufficient as a proof, you can just draw two Venn diagrams for the cases where A and B are disjoint or have an overlap and show that if you shade the left hand side or the right hand side, you will get the same shaded area. (I personally wouldn't consider that a real hard proof, however).
Do you know how to indicate the different components in a Venn diagram (e.g. union, complement, etc)?
this proof is to show why the two pictures/diagram are the same...