About generalization in mathematics (III). On the inclusion and exclusion principle

Let A1,A2, …,An be finite sets and m(Ai) denote the number of elements of the set Ai. In this paper we obtain a formula of type ”the inclusion and exclusion principle” (Boole-Sylvester) for finding out the number of elements of the set A1?A2?…?An where A?B =(A\B) ? (B\A) is ”the symmetric difference of the sets A and B”: m(A1?A2?…?An)= = n  i=1 m(Ai) ? 2  1?i