1.

For any sets A and B, prove that : (i) (A -B) cap B=phi (ii) A cup (B-A) =A cup B (iii) (A-B) cup (AcapB)=A (iv)(A cup B) -B = A-B (v) A- (A cap B) =A-B

Answer»

SOLUTION :(i) `(A-B) cap B =(A cap B') cap B = A cap(B' cap B) =A cap phi =phi`.
(ii) `A CUP (B-A )=A cup (B cap A') =(A cup B) cap (A cup A') =(A cup B) cap U=(A cup B)`.
(iii)` (A -B) cup (A cap B) =(A capB') cup (A cap B) =A cap (B'cup B)=A cap U=A`.
(IV) `A cup B) -B=(ACUP B) cap B'=(A cap B') =(A cap B') cup ( B cap B') =(A cap B') cup phi =ACAP B ' =A-B`
(v) ` A - (A cap B) =A cap (A cap B) '=A cap (A'cup B' ) =(A cap A') CUP (A cap B') =phi cup (A cap B') =(A cap B') =(A-B)`.


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