CS173 Discrete Mathematical Structures
Fall 2006
Homework #2
due Sunday, September 10, 2006, 8:00 a.m.
1. Post to the class Wiki your favorite saying on the page designated “Welcome!
Post your favorite saying (adage/maxim) here!” Be sure to give credit where it’s
due, but also post your own name as the submitter.
2. Are the following valid arguments? Explain using the rules of inference. Is there
a particular fallacy that is violated?
a. If you agree with me, then you will vote for me.
You vote for me.
Therefore, you agree with me.
b. Everyone who eats fruit every day is healthy.
Christine is not healthy.
Therefore, Christine does not eat fruit every day.
c. If I go swimming, then I will stay in the sun too long.
If I stay in the sun too long, I will sunburn.
Therefore, if I go swimming, then I will sunburn.
d. If x is a real number with x > 2, then x2 > 4.
Suppose that x ≤ 2. Then x2 ≤ 4.
3. Prove by direct proof, using only approved equivalence and inference rules.
Remember to name each rule used.
1. (p q) → r
2. p ¬ r therefore ¬ q
4. Show that if n + 5 is odd, then n is even. Use an indirect proof.
5. Prove that at least one of a, b, and c is greater than or equal to A, where
A = (a + b + c)/3. Use a proof by contradiction.
6. Prove or disprove:
a. ⌈x⌉ + ⌈y⌉ = ⌈x + y⌉
b. ⌊⌈x⌉⌋= ⌈x⌉