Logic Theory — Truth Tables

Part III — Intro to the Interdisciplinary Logic Tool

Originally Published On https://www.setzeus.com/

Now equipped with the principles of logic theory as well as basic notation, it’s time to explore the concept of equivalency in logic. Specifically, what makes two compound premises equal?

Two compound premises X & Y are logically equivalent if, for each assignment of truth values to the primitive premises which make up X & Y, the statements X & Y have identical truth values.

That’s a tricky definition to swallow, but it’s the application of this definition that we care about learning. In order to achieve this, we’ll walk through multiple, increasingly-complicated examples. First though, let’s take a detour to learn a bit more about our Excalibur for this journey — one of the most simple, yet powerful tools for logicians to prove logical equivalence: truth tables.

Introduction to Truth Tables

A truth table is a visual tool, in the form of a diagram with rows & columns, that shows the truth or falsity of a compound premise. It’s a way of organizing information to list out all possible scenarios from the provided premises. Let’s start with the most simple example, a truth table depicting a single premise manipulation: a negation (~) of a primitive premise (P)