Language and Notation of Proof

The language and notation of proof is the foundation of the Proof topic in NSW Year 12 Mathematics Extension 2 (NESA outcome ME2-12-01). This subtopic introduces the formal language of proof — including statement, implication, converse, negation and contrapositive — together with the notation for ‘and’ \(P \wedge Q\), ‘or’ \(P \vee Q\), negation \(\neg P\), implication \(P \Rightarrow Q\), and the quantifiers ‘for all’ \(\forall\) and ‘there exists’ \(\exists\).

Students and teachers will cover how to negate statements, form the converse and contrapositive of an implication, use equivalence \(P \Leftrightarrow Q\), and recognise that an implication is equivalent to its contrapositive \((P \Rightarrow Q) \Leftrightarrow (\neg Q \Rightarrow \neg P)\) — the precise language students need to write and read proofs throughout the HSC Extension 2 course.