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Let A, B and C be the sets such that A u...

Let `A`, `B` and `C` be the sets such that `A uu B=A uu C` and `A nn B = A nn C`. show that `B=C`

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Given that `A uu B=A uu C`
`=>`(`A uu B`)`nnC`=(`A uu C`)`nnC`
`=>`(`AnnC`)`uu`(`BnnC`)=`C` [because (`AuuC`)`nnC`=`C`]
`=>`(`AnnB`)`uu`(`BnnC`)=`C`..........(1) [because(`AnnC`)=`AnnB`]
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