Colorado State University

Recitation R17 - Mathematical Proofs
Spring 2015

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.  Even(x) ∧ Odd(y) → Even(x * y)  Hypothesis
    2.  x = 2k , y = 2j + 1             Even and Odd definitions
    3.  (x * y) = (2k * (2j + 1))       Substitution
    4.          = (4kj + 2k)            Algebra
    5.          = (2(2kj + k))          Algebra
    6.  Even(2(2kj + k)) = true         Even Definition
    7.  Even(x * y) = true              Proves hypothesis

Contrapositive Proof

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

Create a file called R17.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 R17.txt to the RamCT drop box.

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