Problem Set 2—Writing Proofs

Purpose

This problem set reinforces your ability to write formal proofs.

Background

This problem set is based on material in section 1.2 of our textbook, a video on proof-writing in ProofSpace, and discussions of related topics from our September 7 and 9 class meetings.

Activity

Write formal proofs for each of the following propositions. Your proofs should be word-processed (i.e., not hand-written) and should follow the guidelines in Sundstrom’s text.

Proposition 1

The proposition from exercise 2a in section 1.2 of Sundstrom’s text (if x and y are even integers, then x + y is an even integer).

Proposition 2

The proposition from exercise 4b in section 1.2 of Sundstrom’s text (if m is an odd integer, then 5m + 7 is an even integer).

Proposition 3

The proposition from exercise 11a in section 1.2 of Sundstrom’s text (if a, b, and c are real numbers such that the polynomial ax² + bx + c has roots x₁ and x₂, then x₁ + x₂ = -b/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.