Session 5: Proof Techniques

Overview

Working session on proof technique and mathematical writing.

Lecturer

Omar Sinno (ECE)

Session Information

• Date and Time: Monday 5 October 2026 — 17:30-19:30
• Place: (to be announced)
• Online Meeting Link
• Session Recording

Core Concepts

• Direct proof; contraposition; proof by contradiction
• Proof by cases and exhaustion; biconditionals; uniqueness; counterexamples
• Existence proofs: constructive vs non-constructive
• Writing mathematical prose: what “let”, “suppose”, “consider”, “it suffices to show”, “WLOG” and others mean
• Common mistakes: assuming the conclusion, division by zero, unjustified WLOG, etc.
• Locating the defects in a flawed proof for practice

Slides

Session 5 Slides: Download PDF

Readings

• Book of Proof (Hammack), Ch. 7, 8, 9
• Mathematics for Computer Science, Ch. 2

Exercises & Extra Steps

• Practice (not collected): prove that if n² is even then n is even, by contrapositive and then by contradiction
• Practice (not collected): prove √2 is irrational, then identify the step that would break for √4
• Problem Set 1 due today — hand it in on paper at the start of the session

Navigation

• ← Previous: S4: Predicate Logic — Quantifiers, Binding, Scope
• Back to Course Overview
• Next: S6: Sets, Relations, Orders, Closures →

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