For any two events A and B prove that `P(A cup B) le P{A) + P (B)`.

For any two events A and b prove that, P(A cap B ) le P(A) le P(A cup B ) le P(A) + P(B)

For any two sets A and B, prove that P(A) cup P(B) sube P(A cup B)

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

For any two sets A and B, prove that P(A cap B) = P(A) capP(B) where P(A) is the power set of A.

For any two events A and b prove that, P(A) ge P(A cap B) ge P(A) + P(B) - 1

For any two events A and B, show that, P(A uu B) = P(A) + P(B) - P(A nn B) .

Foe any two events A and B prove that , P(A)geP(AcapB)geP(A)+P(B)-1

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).

For any two events A and B, show that max {P(A),P(B)} le P(A cup B) le min{P(A) + P(B),1} Where A cup B, A cap B, max{P(A), P(B)} and min {P(A)+P(B),1} are the occurence of A and B, occurence of A and B both, maximum of P(A) and P(B): minimum of P(A) + P(B) and 1 respectively.

For twos events A and B if P(A cup B) = (3)/(4) , P(A cap B) = (1)/(4), P(A) = (2)/(3) then P(bar(A) cap B) =