Propositional Forms

Abstract

Consider the proposition ¬ 3 < 2 ∧ (2 × 3 = 7 ∨ 0 < 5). In Chapter 2 we saw that it can be obtained as an instance of P ∧ Q by substituting ¬ 3 < 2 for P and 2 × 3 = 7 ∨ 0 < 5 for Q. However, it can also be obtained as an instance of ¬P ∧ (Q ∨ R) with P, Q and R replaced by the atomic propositions 3 < 2, 2 × 3 = 7 and 0 < 5 respectively. Yet another possibility is to start with P ∧ (Q ∨ R), and to replace P by the negation ¬ 3 < 2. Expressions such as ¬P ∧ (Q ∨ R) and P ∧ (Q ∨ R) play an important part in logic and are known as propositional forms.