Homework 2
Due Friday, September 22 at the start of class.
- Prove the following statements, assuming that all the named sets
are subsets of a fixed universe E:
- A and B are disjoint iff A < B'.
- A = Ø iff (A ^ B') U (A' ^ B) = B.
- (A - B) U (A - C) = A - (B ^ C).
- (B - A) U (C - A) = (B U C) - A.
- ^ P(A) = Ø.
- P(A) ^ P(B) = P(A ^ B).
- P(A) U P(B) < P(A U B).
- 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.)