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For any two sets A and B, prove that : ...

For any two sets A and B, prove that :
(i) `(A capB)cup(A-B)=A`
(ii) `A cup(B-A)=A cupB`.

Text Solution

Verified by Experts

(i) `(A capB)cup(A-B)`
`=A(capB)cup(AcapB')(because A-B=AcapB')`
`= A cap(BcupB')` (From distributive law)
`= A capU` (U=universel set)
`=A`
(ii) `A cup(B-A)`
`=A cup(BcapA')(becauseB-A=BcapA')`
`=(A cupB)cap(A cupA')` (From distributive law)
`= (A cupB)capU` (U = universal set)
`= A cupB`.
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