Methods of Proof (Contradiction & Counterexamples)

Methods of proof builds on the Proof topic in NSW Year 12 Mathematics Extension 2 (NESA outcome ME2-12-01). This subtopic shows how to establish a claim by proof by contradiction — assuming the opposite and reaching an impossibility — and how a single counterexample is enough to show that a general claim is false.

Students and teachers will cover direct and contrapositive proofs about integers — odd and even numbers, divisibility, and the irrationality of numbers such as \(\sqrt{2}\) — and how to set out each argument clearly, as required in the HSC Extension 2 course.