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Prove that : (A-B) nn (B-A)=phi....

Prove that : `(A-B) nn (B-A)=phi`.

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Prove that : (A-B) nn (A nn B)=phi .

Prove that : A nn(B-A)=phi .

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For sets A,B and C, prove that : (A-B)nn C=(A nn C)-B .

Prove that following : (A nn B=phi) iff A sub B^(c) implies B sub A^(c) , where U is the universal set.

If A and B are any two sets, prove that : A-B =A nn B^(c) .

Prove that : (A uu B)=(A-B) uu (B-A) uu (A nn B) .

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If A, B and C are any three sets, then prove that : A nn (B-C) = (A nn B)-(A nn C) .

For any four sets A, B, C and D, prove that : (A nn B)xx (C nn D)= (AxxC) nn (BxxD) .