If A,B,C are three events associated with a random experiment, prove that

P(A U B U C) = P(A) +P(B)+P(C)-P(A intersection B) - P(A intersection C) - P(Bintersection C) + P(A intersection B intersection C)

P (A ∪ B ∪ C) = P [(A ∪ B) ∪ C]

= P (A ∪ B) + P (C) – P [(A ∪ B) ∩ C]                      [P (X ∪ Y) = P (X) + P (Y) – P (X ∩ Y)]

= P (A ∪ B) + P (C) – P (A ∩ C) – P (B ∩ C)             [P (X ∪ Y) ∩ Z] = [P (X ∩ Z) ∪ P (Y ∩ Z)]]

= P (A) + P (B) – P (A ∩ B) + P (C) – P (A ∩ C) – P (B ∩ C)

= P (A) + P (B) + P (C) – P (A ∩ B) – P (B ∩ C) – P (A ∩ C)