For any two events A,B shows that
`P(AcapB)-P(A)P(B)=P(A^(C))P(B)-P(A^(C)capB)`
`=P(A)P(B^(C))-P(AcapB^(C))`

For any two events A and B, shows that P(A^(C)capB^(C))=1" +"P(AcapB)-P(A)-P(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.' C show that P(AcupBcupC)=P(A)+P(B)+P(C)-P(AcapB)-P(BcapC)-P(CcapA)+P(AcapBcapC)

For any sets A and B , prove that : P(AcapB)=P(A)capP(B) .

If A,B are two events, then show that P((A)/(B))P(B)+P((A)/(B^(C)))P(B^(C))=P(A).

If A, B are two events, then show that (i) P((A)/(B))P(B)+P((A)/(B^(C )))P(B^(C ))=P(A) (ii) P(A^(c )|B^(c ))=(1-P(AuuB))/(1-P(B)),P(A) gt 0, P(B) ne 1 (iii) P(A//B^(C ))=(P(A)-P(AnnB))/(-P(B)),P(B^(C )) gt 0