November 2025
Beginner
416 pages
8h 6m
English
Content preview from Logic For Dummies, 2nd Edition
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Chapter 6
Turning the Tables: Evaluating Statements with Truth Tables
IN THIS CHAPTER
Creating and analyzing statements by using truth tables
Applying truth tables to evaluate tautologies, contradictions, and contingencies
Seeing the connections between statement types and evaluations
In this chapter, you discover one of the most important tools in sentential logic (SL): the truth table. Truth tables enable you to evaluate a statement under every possible interpretation (a fixed set of truth values for all statement constants; see Chapter 5), which in turn provides insight about a statement even when you don’t know the truth values of its constants.
Truth tables open up vast new logical territory. First of all, they’re an easy way to find out when a statement is true or false — a central question in logic. But beyond this, they can help you identify tautologies and contradictions (statements in SL that are always true or always false).
You can also use truth tables to decide whether a set of statements is consistent — that is, whether all the interpretations can be true. Additionally, with truth tables, you can figure out whether two statements are semantically equivalent — that ...
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I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.