Language and Notation of Proof

Language and notation of proof opens the Proof topic in NSW Year 12 Mathematics Extension 2 (NESA outcome ME2-12-01). Students learn the vocabulary used to state and link claims — statement, implication, converse, negation and contrapositive — together with the symbols \(P \wedge Q\) for ‘and’, \(P \vee Q\) for ‘or’, \(\neg P\) for ‘not’, \(P \Rightarrow Q\) for ‘implies’, and the quantifiers \(\forall\) (‘for all’) and \(\exists\) (‘there exists’).

Students and teachers will cover negating statements (including quantified ones), writing the converse and contrapositive of an ‘if…then’ claim, using ‘if and only if’ \(P \Leftrightarrow Q\), and seeing why \(P \Rightarrow Q\) and \(\neg Q \Rightarrow \neg P\) always share the same truth value, so a contrapositive argument is a valid proof — the precise language behind every proof in the HSC Extension 2 course.