Prove that `AuuB=AnnB` if and only if `A=B`

Prove that A-B=AnnB^(c ) .

Prove that (AuuB)-(AnnB) is equal to (A-B)uu(B-A) .

For any two sets Aa n dB , prove that (AuuB)-B=A-B (ii) A=(AnnB)=A-B (iii) A-(A-B)=AnnB (iv) Auu(B-A)=AuuB (A-B)uu(AnnB)=A

Prove that (AuuBuuC)nn(AnnB'nnC')'nnC'=BnnC'

If A, B are two sets, prove that AuuB=(A-B)uu(B-A)uu(AnnB) . Hence or otherwise prove that n(AuuB)=n(A)+n(B)-n(AnnB) where, n(A) denotes the number of elements in A.

For any two events A and B associated to a random experiment, prove that: P(A)=P(AnnB)+P(AnnbarB) , P(B)=P(AnnB)+P( barAnnB) , P(AuuB)=P(AnnB)+(AnnbarB)+P(barAnnB)

If Aa n dB are two sets, then (A-B)uu(AnnB) is equal to (a) AuuB (b) AnnB (c) A (d) B

If A and B are two independent events, prove that P(AuuB).P(A'nnB')<=P(C) , where C is an event defined that exactly one of A and B occurs.

If A and B are two independent events, prove that P(AuuB).P(A'nnB')<=P(C) , where C is an event defined that exactly one of A and B occurs.

If two subsets A and B of set S containing n elements are selected at random, then the probabit AnnB=phi and AuuB=S is