CSE 321 Assignment #3
Autumn 1998

Due: Friday, October 16, 1998.

Reading assignment: Read the text, Discrete Mathematics and Its Applications, Sections 2.3, 3.1 and read the Supplementary Logic Notes. We will begin in section 3.1 and refer back to section 2.3 as needed. The following problems are from the Third Edition of the text.

Practice Problems:

Problems:

  1. Section 1.3, page 35, Problem 12.

  2. Section 1.3, page 35, Problem 14.

  3. 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.

  4. Section 1.3, page 36, Problem 20.

  5. Section 3.1, page 181, Problem 8. Instead of part (b), give an indirect proof of the following: "If n squared is odd then so is n." (See the bonus.)

  6. Section 3.1, page 181, Problem 10

  7. Section 3.1, page 181, Problem 12

  8. Prove or disprove that n*n + 3*n + 1 is always prime.

  9. (Bonus) Section 3.1, page 181, Problem 8 (b) as given.

  10. (Bonus) Section 3.1, page 182, Problem 32