So for the union of A1 and A2 .. A1 u A2 = A1 + A2 - A1 n A2

Prove by induction that it is true for all Unions

So i start with another Union A3 so,

A1 u A2 u A3 = A1 + A2 +A3 - (A1 n A2) - (A1 n A3) - (A2 n A3) + (A1 n A2 n A3)

now i want to to prove for n+1. or for all unions

How would i do this?