If A,B,C are any three sets prove that `A sub B implies A xx C sub B xx C`

Prove that A sub phi implies A =phi .

Prove that A sub B,B sub C implies A sub 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) .

For any three sets A, B,C prove that : (A- B) xx C= (AxxC) - (BxxC) .

For any three sets A, B,C prove that : (A nn B) xx C= (AxxC) nn (BxxC) .

If vec a,vec b,vec c are any three vectors, prove that vec a xx (vec b xx vec c) +vec b xx(vec c xx vec a)+ vec c xx(vec a xx vec b) = vec 0

If A, B, C are three matrices of the same order, then A = B implies A + C = B + C .

For any three sets A, B, C, prove that : Axx(B - C)=(A xx B)- (Axx C) .