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

Show that for any sets A and B,`A = (A nnB) uu(A- B )`and `A uu(B - A) = (A uuB)`

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(i)`A = (A nnB) uu(A - B )`
consider RHS=`(A nnB) uu(A - B )`=`(A nnB) uu(A - B' )`(by definition of difference of sets,`A-B=AnnB'`)
=`Ann(BuuB')` (by distributive property)
=`AnnU` (Therefore `AuuA'=U`)
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