---
tag: 05RSK4Q657
kind: concept
name: Truth table
msc: [03B05]
uses: [0XR7A7RSXB, 0M28ASWG8T, 0H5GKDTB01, 0ZNX6DQ3EJ]
sources:
  - url: https://en.wikipedia.org/wiki/Truth_table
    locator: lead section
same_as:
  wikidata: Q219079
  wikipedia: Truth table
---

## Summary

A truth table is a table that gives the truth value of a compound [[proposition|0ZGC7ZESYN]] for each assignment of truth values to its variables.
Each row of the table is one assignment, and the last column gives the value of the compound proposition.
A proposition with $n$ variables has a truth table with $2^n$ rows.

## Remarks

The truth tables of [[negation|0XR7A7RSXB]], [[conjunction|0M28ASWG8T]], [[disjunction|0H5GKDTB01]], [[implication|0ZNX6DQ3EJ]] and the [[biconditional|0V6GAWTBYW]] define these connectives.
A proposition is a [[tautology|0D1AHYPM8N]] when its column has only the value true.
Two propositions are [[logically equivalent|06GYGS41JK]] when their columns are the same.

## Explanations

### L1 human

A truth table lists every possible case.
For $p \land q$ there are four cases, because $p$ and $q$ each have two values.
You compute the value of the whole formula in each case, one row at a time.