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If A, B, C are three events associated w...

If A, B, C are three events associated with a random experiment prove that `P(AuuBuuC)=P(A)+P(B)+P(C)-P(AnnC)-P(BnnC)+P(AnnBnnC)`

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Let P(E) denote the probability of occurrence of event E. If A and B are two events associated with an experiment such that |[P(A)-1,P(B),-P(A nn B)],[P(B),-P(A nn B),P(A)-1],[-P(A nn B),P(A)-1,P(B)]|=0 then (A) P(A uu B)=1 (B) P(A/B)=(P(A)+P(B)-1)/(P(B)) (C) if A sub B then P(B)=P(A uu B) (D) if A sub B then P(A)=1