The Concept

A truth table is a systematic enumeration of all possible truth value assignments to a set of variables, together with the resulting truth value of a logical expression under each assignment.

Truth tables serve two purposes:

1. Definition — they fully define what a logical operator or expression means. No ambiguity is possible. The table says what the output is for every input.
2. Verification — given two expressions claimed to be equivalent, you build both tables and compare them column by column. If they match on every row, the expressions are equivalent (Chapter 4).

The visual model: a truth table is a switch-and-circuit diagram flattened into a table. Every row is one configuration of all switches. The output column shows whether current flows (True) or not (False) through the circuit for that configuration.