Truth table

Summary

A truth table is a table that gives the truth value of a compound proposition 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, conjunction, disjunction, implication and the biconditional define these connectives. A proposition is a tautology when its column has only the value true. Two propositions are logically equivalent 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.