1.

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

Answer» `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)`
`= (AuuB) nn (bar(A nn B))` (As `(barAuubarB) = bar(A nn B)`)
Again using `A-B = AnnbarB`,
`= (A uu B) - (AnnB) = L.H.S.`


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