For any three sets A,B C, prove that :
`n(AuuBuuC)=[n(A)+n(B)+n(C)+n(AcapBcapC)]-[n(AcapB)+n(BcapC)+n(AcapC)]`.

If A , B and C are any three sets , then prove that : Acap(B-C)=(AcapB)-(AcapC) (ii) Acap(BDeltaC)=(AcapB)Delta(AcapC) .

Given that n(A)=25,n(B)=15, n(AuuB)=10 . Determine n(AcapB)

If A , B and C are three non - empty finite sets such that n (A) =19 , n (B) = 15 , n (C ) =17, n(capB)=11,n(BcapC)=6,n(CcapA)=7andn(AcapBcapC)=5 . Also n (U) =50. (i) n(AcapB^(c)capC^(c)) (ii) n(BcapC^(c)capA^(c)) (iii) n(CcapA^(c)capB^(c)) (iv) n(CcapBcapC^(c)) (v) n(BcapCcapA^(c)) (vi) n(CcapAcapB^(c)) (vii) n(AuuBuuC) (viii) n((AuuBuuC)^(c)) .

If A and B are two non empty sets the prove the following1.n(AuuB)=n(A)+n(B)-n(AnnB) ." " 2. nAuuBuuC)=n(A)+n(B)+n(C)-n(AnnB)-n(BnnC)-n(Cnna)+n(AnnBnnC)

If A,B,C are subsets of the universal set U such that n(U)=692,n(B)=230,n( C)=370,n(BcapC)=20,n(A' cap B'capC')=10 then: n(AcapB'capC')=

If A and B are subsets of the universal set E such that n( E)=50,n(A)=35,n(B)=22 and n(A'capB')=3, then: n(AcapB) and n(AcupB) are respectively

If A and B are two sets such that n(A)=12, n(B)=19 and (A cup B)=26 then find. (a) n(A cap B) (b) n(A-B) (c) n(B-A)

If n(A)=3,n(B)=5 and n(AcapB)=2, then: n(AxxB)=

Let A and B be two sets such that : (i) n(A)=20,n(AuuB)=42andn(AcapB)=4 (ii) n(A)=17,n(AuuB)=38andn(AcapB)=2 . Find n (B) , n (A-B) and n (B-A).

If n (A)=n(B) , find n (AcapB)andn(AuuB) use the fig