If A and B are any two sets, then prove that `(a-B)nnB = phi`

If A and B are any two matrics then

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

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

If A and B are any two sets, prove that P(A) = P(B) implies A = B.

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

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

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

If vec a and vec b are any two vectors, then prove that |quad vec a+ vec b|^2 + |quad vec a- vec b|^2= 2|quad vec a|^2 + 2|quad vec b|^2 .

If A and B are two sets, then A nn (A uu B) equals