Logic For Dummies, 2nd Edition

Chapter 17

Proving Arguments with QL

IN THIS CHAPTER

Comparing proofs in SL and QL

Applying quantifier negation in QL

Writing QL proofs using the four quantifier rules: UI, EI, UG, and EG

Here’s the good news: If you’ve got the hang of sentential logic (SL) proofs, you already know 80 percent of what you need to write proofs in quantification logic (QL). So, first you should figure out how much you already grasp about proof writing. If you want a refresher, take a look at the chapters in Part 3, which tell you everything you need to know.

In this chapter, I illustrate how proofs in QL are similar to those in SL. One way they’re similar is that they both use the eight implication rules (see Chapter 9) and the ten equivalence rules (refer to Chapter 10). I explain exactly how and when to use these rules.

After you get comfortable with a few simple proofs in QL, I introduce an additional rule, quantifier negation (QN), which allows you to make changes that affect the universal or existential quantifiers ( or ). Luckily, this rule, which is the first rule that’s unique to QL, is an easy ...