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# 80-110 Nature of Mathematical Reasoning

Spring 2002

Dirk Schlimm

Homework 12

Wednesday, April 17

Due Monday, April 22

1. Set theory. (5 points)

Read FOL, pages 207-224 (Chapter 8). Solve the following problems:

1. Page 211, Problem 4.
2. Page 217, Problems 13 and 14.
3. Page 218, Problem 18.
4. Page 220, Problem 19.

This chapter is pretty technical and difficult at times, but the homework problems are rather basic. To solve them you don't need to understand the proofs and first-order formalizations! I suggest you first look at the problems, and then glean what you need to know to solve them.

If you are interested in knowing more about Russell's Paradox and modern set theory, make sure you read sections 8.8-10!

2. 1-1 Functions. (2 points)

Take a set A={alligator, bear, chimpanzee} and a set B={apple, banana, cherry}. Write down two functions from A to B, one of which is 1-1 and one which is not.

3. Cardinality. (3 points)

Prove: The cardinality of the set of even numbers is the same as the cardinality of the set of natural numbers.