Prove that `A uuB = A iff A sup B`

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

Prove that: AsubeB iff B'subeA'

Prove that if A uu B=C and A nn B=phi , then A= C-B.

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

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

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

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