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

Prove that A uu B= A nn B implies A=B.

Prove that A sub phi implies A =phi .

Prove that A sube B and C sube D imply : (A xxC) sube (B xxD) .

Prove the following : B sub A implies A uu B=A .

Prove that : (i) A sub (A uu B) (ii) B sub (A uu B) .

Whether the following statement is true ? Justify your answer. If A sub B and B sub C,then A sub C.

AB=AC implies B=C .

In the following, determine whether the statement is true or false. If it is true, prove it. If it is false, give an example. If A sub B and B sub C , then A sub C

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