Prove that `A nnB = A iff A sub B`

Prove that: AsubeB iff B'subeA'

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

Prove that If B sub A and if B has one element less than that of A, prove that A has twice as many subsets as B.

Prove that : z= bar(z) iff z is real.

Let A and B be two sets. Prove that : (A -B) uu B= A if and only if B sub A .

Prove that : z= -bar(z) iff z is either zero or purely imaginary.

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