Colorado State University

Recitation R14 - Mathematical Proofs
Spring 2014

CS160: Foundations in Programming

The purpose of this lab is to:

Direct Proof

 The TA will 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

Contrapositive Proof

 Solve the following mathematical proof on your own, using the contrapositive:

Create a file called R14.txt for your proof, using the same format as above.

Show that if xy is even then x or y is even.

Show your proof to the TA and submit R14.txt to the RamCT drop box.
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