A truth table is a tool to illustrate the outcomes of a proposition. Each column refers to a proposition (or atom) while each row refers to a possible permutation of only the atoms. Truth tables are a useful way to illustrate simple statements, but become exponentially more difficult to draw as the number of atoms increase.
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When using multiple propositions, all possible permutations of values must be considered, resulting in rows, where is the number of atoms. The truth table below uses 3 atoms, having rows.
| T | T | T |
| T | T | F |
| T | F | T |
| T | F | F |
| F | T | T |
| F | T | F |
| F | F | T |
| F | F | F |