Logic For Dummies, 2nd Edition

Chapter 9

Providing Proof for What You Propose

IN THIS CHAPTER

Introducing formal direct proofs

Constructing proofs using the implication rules of inference

Understanding the if, and, or, and double-if rules

You may already have some experience writing proofs, like those tricky problems that were an important part of high school geometry. In geometry proofs, you started with a set of simple axioms (or rules, also called postulates), such as “All right angles are equal,” and figured out how to build toward more complex statements called theorems.

Computer programming, in which you use simple statements to create complex software, also resembles the proof method. And the idea of complexity arising out of simplicity is common to proofs in sentential logic (SL) as well.

In a sense, constructing a proof is like building a bridge from one side of a river to the other. The starting point is the set of premises you’re given, and the end point is the conclusion you’re trying to reach. The pieces you use to build the bridge are the rules of inference, a set of 18 ways to turn old statements into new ones.

In this chapter, I introduce you to the first eight rules of inference — the set of ...