Lecture: Proof by Contradiction

Background Material

• Natural Deduction
• Proofs encountered in various math courses.

Reading

• Chapter 4 of CMU OLI text.

Topics

• Motivating example
  • Rational numbers and repeating decimals
  • Irrationality of sqrt(2)
• Negation rules
• Example indirect proofs in natural deduction

Lecture Notes

• indirect.pptx or indirect.pdf

Programs

• LogicLab

Resources

• None.

Assignments

• Practice using LogicLab.
  1. Prove DeMorgan's laws
  2. Prove the definition of the conditional
  3. Prove law of excluded middle
• Quizzes and problem sets following chapter 4 of the CMU OLI text. Due Fri. Apr. 22 at 11:59 pm.