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Prove that : (i) (AuuBuuC)^(c)=A^(c)ca...

Prove that :
(i) `(AuuBuuC)^(c)=A^(c)capB^(c)capC^(c)`
(ii) `(AcapBcapC)^(c)=A^(c)uuB^(c)uuC^(c)`
(iii) `(AuuB)=(A-B)uu(B-A)uu(AcapB)`.

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Prove (AcapB)^(c)=A^(c)uuB^(c) .

(a) If U= {1,2,3,……, 10} ,A = { 1,2,3,4,5}, B= {1,3,5,7,9} , C {2,4,8,10}, verify that : (i) (AuuB)^(c)=A^(c)capB^(c) (ii) (AcapB)^(c)=A^(c)uuB^(c) (iii) A-B=AcapB^(c) (iv) Acap(BuuC)=(AcapB)uu(AcapC) . (b) If U={1,2,3,4,5,6,7,8,9}, A={2,4,6,8} and B= {2,3,5,7}. Veify that : (i) (AuuB)^(c)=A^(c)capB^(c) (ii) (AcapB)^(c)=A^(c)uuB^(c) .

Prove that : (i) A^(c) - B^(c)=B-A (ii) B^(c)-A^(c)=A-B .

(i) (AuuB)^(c) =…………… (ii) (AcapB)^(c) = …………….

Prove that (AuuB)-(AcapB)=(A-B)uu(B-A) .

For any 3 sets A, B and C, prove that : (i) A-(B cupC)=(A-B)cap(A-C) (ii) A-(BcapC)=(A-B)cup(A-C) (iii) A cap(B-C)= (A cap B) - (A cap C) (iv) (A cupB)-C=(A-C)cup(B-C) (v) A cap (B DeltaC)=(A capB)Delta(A capC) .

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)) .

Prove that (A uu B)xx C=(A xx C)uu(B xx C)

Let U={1,2,3,4,5,6,7,8,9},A = {2,4,6,8} and B={2,3,5,7} . Verify that : (i) (AuuB)^(c)=A^(c)capB^(c) (ii) (AcapB)^(c)=A^(c)uuB^(c) .