Colorado State University

Recitation R13 - Mathematical Proofs
Fall 2013

CS160: Foundations in Programming

The purpose of this lab is to:

See the TA present the following mathematical proof

 Show that xy is even when x is an even integer and y is an odd integer. 
        Step                        Reason
    1.  E(x) ∧ O(y) → E(x * y)      Hypothesis
    2.  x = 2k , y = 2j + 1         Even and Odd definitions
    3.  E(2k * (2j + 1))            Substitution
    4.  E(4kj + 2k))                Algebra
    5.  E(2(2kj + k))               Algebra
    6.  E(2(2kj + k)) = true        Even Definition (2 * anything is even)
    7.  E(x * y) = true             Proves hypothesis

Work on RamCT Quiz 4 with help from the TA

Solve the following logic proof on your own (optional):

 Use the Rules of Inference and state the specific rule used for each step.
  1. Given: Prove: q

  2. Given: Prove: ¬D

  3. Given: Prove: (q ∧ p)

  4. Given: Prove: C

Answers will be posted next week on the course website.
Checkin with the TA and show your score on RamCT Quiz 4 to get credit for this lab.
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