Spring 2015

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!

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

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.