Recitation R17 - Mathematical Proofs Spring 2015

CS160: Foundations in Programming

The purpose of this lab is to:
• Have a direct mathematical proof presented to you
• Practice writing a contrapositive mathematical proof yourself.
• Possibly get help with the second math homework!

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.