Logic table

A logic table, more commonly called a truth table, is a two-dimensional array that enumerates every possible combination of truth values for the variables in a logical formula.

Each row represents one unique assignment of true or false to each variable, along with the resulting evaluation of the formula for that assignment.

The rows are ordered by counting in binary, so a formula with three variables will produce eight rows (2³), progressing systematically through all combinations from 000 to 111.

Logic tables are a fundamental tool in propositional logic and digital circuit design. They make it straightforward to verify whether a formula is a tautology (true in every case), a contradiction (false in every case), or contingent (true in some cases and false in others).

They are also used to compare formulas for logical equivalence: two formulas are equivalent if and only if their truth tables are identical.