## Foundations of Mathematics## Mathematical and Formal Logic |

## What is a truth table? |

A truth table is a two-dimensional array of truth values derived by determining the validity of arguments through assigning all possible combinations of truth values to the statements. This simple form of logic depends on a combination of certain statements, using terms such as “not” or “and,” along with the input values.

The first columns correspond to the possible input values and the last columns to the operations being performed; the rows list all possible combinations of true (T) or false (F) inputs, together with the corresponding outputs. The following is a truth table for the three most common binary operations of logic (“if…then,” “or,” “and”), using *s* and *t* as the statements: