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Show that for any sets A and B, A=(AnnB)...

Show that for any sets A and B, `A=(AnnB)uu(A-B)` and `Auu(B-A)=AuuB`

Text Solution

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(i) `A=(A∩B)∪(A−B)`
Consider RHS`=(A∩B)∪(A−B)`
`=(A∩B)∪(A∩B′) ` (by def of difference of sets, `A−B=A∩B′`)
`=A∩(B∪B′)` (by distributive )
`=A∩U (∵A∪A′=U)`
`=A`
`=LHS`
...
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