# CSE 321 Assignment #2Spring 2001

### Due: Friday, April 13, 2001 at the beginning of class.

Reading assignment: Read the text, Discrete Mathematics and Its Applications, sections 3.1 and 2.3 and read the supplementary logic notes. The following problems are from the 4th edition of the text. They have the same numbers in the 3rd edition of the text unless otherwise noted.

Practice Problems answered in the back of the book: Section 1.1, problems 7, 15, 35 (3rd edition 27); Section 1.2, problems 7, 9, 25; Section 1.3, problem 9 (3rd edition 7)

Problems:

1. Section 1.3, Problem 12. (Problem 10 in 3rd edition)

2. Section 1.3, Problem 18. (Problem 12 in 3rd edition)

3. Section 1.3, Problem 22. (Not in 3rd edition)

4. Show that the formula FORALL x (P(x) -> Q(x)) is not logically equivalent to the formula FORALL x P(x) -> FORALL x Q(x). Give examples of predicates P and Q and an associated universe which demonstrate that the two expressions are not equivalent.

5. Section 1.3, Problem 34. (Problem 20 in 3rd edition)

6. Section 3.1, Problem 16. (Problem 8 in 3rd edition). Instead of part (b), give an indirect proof of the following: "If n squared is odd then so is n." (See the bonus.)

7. Section 3.1, Problem 20. (Problem 10 in 3rd edition).

8. Section 3.1, Problem 68. (Not in 3rd edition)

9. Prove or disprove that n*n + 3*n + 1 is always prime for integer n > 0.

10. (Bonus) Section 3.1, Problem 16 (b) as given. (Problem 8 (b) in 3rd edition.)

11. (Bonus) Section 3.1, Problem 48. (Not in 3rd edition)