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Using properties of sets, show that (i)...

Using properties of sets, show that (i) `A uu ( A nn B) = A` (ii) `A nn (A uu B) =A`.

Text Solution

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(i) `Acup(A capB)=(A cupA)cap(AcupB)`
`=A cap(A cupB)`
`=A" "[becauseA sube A sub B]`
Therefore, `A cup (A cap B)=A`
(ii) `A cap (A cup B)=(A cap A) cup (A cap B)`
`= A cup (A capB)`
`= A[because (A cap B) sube A]`
Therefore, `A cap (A cup B)=A`.
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