- Mathematical Proofs
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!
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.
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
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.
© 2015 CS160 Colorado State University. All Rights Reserved.