Direct proof: Assume \(p\) is true and show that \(q\) is true.
Proof by contradiction: For \(p \implies q\), assume \(p\) is true and \(q\) is false, and show that this leads to a contradiction.
Proof by contrapositive: For \(p \implies q\), prove \(\neg q \implies \neg p\) instead.
Proof by induction: For statements involving natural numbers, prove the base case and then show that if the statement holds for \(n\), it also holds for \(n+1\), which is called the inductive step.
Proof by cases: Break the statement into several cases and prove each case separately.
F.3 Resources
L. V. Snyder and Z.-J. M. Shen, Fundamentals of supply chain theory, 2nd ed. Nashville, TN: John Wiley & Sons, 2025.
How to Prove It: A Structured Approach by Daniel J. Velleman, website
Mathematical Reasoning Writing and Proof, Version 3 by Ted Sundstrom, website