# 2   Propositional natural deduction

We begin the study of natural deduction by looking at the rules governing the connectives  AND  and  IMP  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  NOT  and  OR  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.

The exercises in this chapter are best approached using the proof editing tool provided.

• Natural deduction rules ANDI and ANDE
• The rules IMPI and IMPE; discharging assumptions
• Theorems, weakening and contraction
• Proofs using conjunction and implication
• Natural deduction rules NOTI and NOTE; using RAA instead
• RAA is equivalent to NOTI and NOTE
• Natural deduction rules ORI and ORE
• Proofs using negation and disjunction

• Sample problems with solutions