Problem Set 1—Propositions

Purpose

This problem set reinforces your understanding of propositions (i.e., mathematical statements) and of their truth or falsehood.

Background

This problem set is based on material in section 1.1 of our textbook. We discussed that section in class on January 20.

Activity

For each of the following sentences, determine whether it is or is not a mathematical statement. For each that is a statement, decide whether it is true or false. Give a brief reason, although not a formal proof, why you classify it as true/false:

1. Every even number is a multiple of 2.
2. Winter is a nicer season in Geneseo than summer.
3. More than half of Earth’s atmosphere by volume is nitrogen.
4. x is a real number.
5. There is some real number that is greater than 7.
6. There is some real number, x, such that x > 7.
7. There is some real number, x, such that x > y.
8. If 1 < 2 then Engl 342 is a prerequisite for Math 239.
9. If Engl 342 is a prerequisite for Math 239 then 1 < 2.
10. For all real numbers x, if Engl 342 is a prerequisite for Math 239 then calculating 3x + 1 will cause a genie to appear and grant you three wishes.

Follow-Up

I will grade this exercise in a face-to-face meeting with you. During this meeting I will look at your solution, ask you any questions I have about it, answer questions you have, etc. Please bring a written solution to the exercise to your meeting, as that will speed the process along.

Sign up for a meeting via Google calendar. Please make the meeting 15 minutes long, and schedule it to finish before the end of the “Grade By” date above.