# Wolfram Language & System 11.0 (2016)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.
BUILT-IN WOLFRAM LANGUAGE SYMBOL

# BooleanTable

BooleanTable[bf]
gives a list of truth values for all possible combinations of variable values supplied to the Boolean function bf.

BooleanTable[expr,{a1,a2,}]
gives a list of the truth values of the Boolean expression expr for all possible combinations of values of the ai.

BooleanTable[expr,{a1,a2,},{b1,},]
gives a nested table of truth values of expr with the outermost level giving possible combinations of the ai.

## DetailsDetails

• The possible combinations of variable values are given in the order Tuples[{True,False},n].
• BooleanTable gives a list or array of True, False values.
• Boole[BooleanTable[]] gives 1, 0 values.
• In BooleanTable[expr,{a1,a2,}] etc. any of the variables in expr that are not explicitly among the ai etc. are left in symbolic form.
• BooleanTable[bf,{r1,r2,}] gives a list of truth values corresponding to possible values of the r1, r2, variables for the Boolean function bf.
• BooleanTable[bf,{r1,},{s1,},] gives a nested table of truth values with the outermost level giving combinations of the ri variables.

## ExamplesExamplesopen allclose all

### Basic Examples  (2)Basic Examples  (2)

The vector of truth values for Or:

 In[1]:=
 Out[1]=

Convert to 1, 0 form:

 In[2]:=
 Out[2]=

2D truth table for Or:

 In[1]:=
 Out[1]//TableForm=