This exercise derives the probability of an arbitrary (non-disjoint) union of events, derives the union bound, and derives some useful limit expressions. (a) For two arbitrary events A1 and A2, show that A UA2 = A1U(A2-A), Show that Aj and A2 - A are disjoint. ne e.r where A2-A1 = A2A. %3D Venn diagrams were invented to help understand expressions like these.