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Using the properties of sets, a show tha...

Using the properties of sets, a show that `Acup B-AcapB=(A-B) cup (B-A)`

Text Solution

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`R.H.S. = (A-B) uu (B-A)`
`=(AnnbarB) uu (B nn barA)` (As `A-B = AnnbarB`)
`=((AnnbarB) uu B) nn ((AnnbarB) uu barA)`
`=((AuuB)nn(BuubarB)) nn ((barA uu A) nn (barAuubarB))`
As, `(barA uu A) = U`(Universal set)
so, our expression becomes,
`=((AuuB)nnU) nn (U nn (barAuubarB))`
`= (AuuB) nn (barAuubarB)`
...
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