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Prove that, if P(A//B)=P(A) then P(A^c/...

Prove that, if `P(A//B)=P(A)` then `P(A^c//B)=P(A^c)`.

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For any two events A and B prove that, P(A//B) lt P(B//A) " if " P(A) lt P(B)

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For any three events A, B and C, prove that. P(A cup B cup C) = P(A) + P(B) + P( C)-P(Acap B) -P(BcapC) - P(CcapA) + P(Acap B cap C).

UNITED BOOK HOUSE-SET 2-EXERCISE
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  3. Prove that, if P(A//B)=P(A) then P(A^c//B)=P(A^c).

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