Math 310 Collected Homework #3: due Friday
1/28/2005
Sets and Functions
1. Does the Trichotomy law hold
for sets? In other words, given two sets A and B, is it true that one of: A 
B, A
B, or A=B must be true?
If yes, give a proof; if no, give a counterexample.
2. Let A={1, 2, 3, 4} List all
elements of P (A). List
all elements of A
A.
3. Suppose A
B. Prove that P (A) P (B)
4. Prove that if AB=AC and 
, then B=C. (Corrected)
5. Prove that A 
(A 
B) = A.
The next 3 problems
are from Problems II
in the textbook:
6. Page 117 problem 11 parts i, iv, and vi.
7. Page 117 problem 12.
8. Page 118 problem 16 parts ii, iii and v.
(You need to prove any
claims of injectivity or surjectivity.
See section 9 for guidelines and examples.)