Homework 2

Due Friday, September 22 at the start of class.
  1. Prove the following statements, assuming that all the named sets are subsets of a fixed universe E:
    1. A and B are disjoint iff A < B'.
    2. A = Ø iff (A ^ B') U (A' ^ B) = B.
    3. (A - B) U (A - C) = A - (B ^ C).
    4. (B - A) U (C - A) = (B U C) - A.
    5. ^ P(A) = Ø.
    6. P(A) ^ P(B) = P(A ^ B).
    7. P(A) U P(B) < P(A U B).
  2. When is it the case that P(A) U P(B) = P(A U B)?

(Note that I am using < for subset, Ø for the empty set, and ^ for both unary and binary intersection. Also, U is union and P is powerset.)