Problem Set 1—Propositions

Purpose

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

Background

This problem set is based on material in sections 1.1 and 1.2 of our textbook. We discussed (or will discuss) section 1.1 in class on August 31, and section 1.2 on September 2.

Activity

Solve each of the following problems:

Problem 1

Which of the following are legal mathematical statements? Be prepared to explain each answer.

1. All horses have four legs
2. For some natural number n, n > y
3. If all horses have four legs, then four is a positive integer

Problem 2

Which of the following statements are true? Be prepared to explain each answer.

1. For all real numbers x, -1 ≤ sin x ≤ 1
2. For all real numbers x and y, x + y = 3
3. For all real numbers x, if x² < 0 then calculating 3x + 1 will cause a genie to appear and grant you three wishes

Problem 3

Problem 8c in section 1.1 of Sundstrom’s text.

Problem 4

Exercise 1b in section 1.2 of Sundstrom’s text.

Problem 5

Exercise 14 in section 1.2 of Sundstrom’s text. This exercise appears under the “Explorations and Activities” heading. The proposition requested in part (b) should be one that summarizes your findings from part (a).

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.