2 Propositional natural deduction
We begin the study of natural deduction by looking at the rules governing the connectives ∧ and → which are intended to be read "and" and "if...then" respectively. After reading the first three sections, make sure you understand the sample proofs using these two connectives, as they require the concepts fundamental to all proofs in the natural deductive style.
We then add the remaining connectives ¬ and ∨ with the introduction and elimination rules governing them. This will complete the deductive account of propositional logic. Work through all of the proofs in this chapter and make sure you understand them. It is important to become fluent in using the natural deduction system at the propositional level before proceeding to any more advanced parts of logic.
- Conjunction Natural deduction rules ∧I, ∧E
- Implication The rules →I and →E; discharging assumptions
- Counting assumptions Theorems, weakening and contraction
- Examples Proofs using conjunction and implication
- Negation Natural deduction rules ¬I and ¬E; using RAA instead
- Disjunction Natural deduction rules ∨I and ∨E
- Examples Proofs using negation and disjunction
- Extra (math) RAA is equivalent to ¬I and ¬E
Propositional proof exercises Sample problems with solutions