BUILT-IN MATHEMATICA SYMBOL

BooleanTable

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

BooleanTable

gives a list of the truth values of the Boolean expression expr for all possible combinations of values of the

.

BooleanTable

gives a nested table of truth values of expr with the outermost level giving possible combinations of the

.

MORE INFORMATION

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 gives , values.

In BooleanTable etc. any of the variables in expr that are not explicitly among the etc. are left in symbolic form.

BooleanTable is equivalent to Fold.

BooleanTable gives a list of truth values corresponding to possible values of the , , ... variables for the Boolean function bf.

BooleanTable gives a nested table of truth values with the outermost level giving combinations of the variables.

EXAMPLES

CLOSE ALL

Basic Examples (2)

The vector of truth values for Or:

Convert to 1, 0 form:

2D truth table for Or:

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=

Scope (6)

Generate a truth table for a Boolean expression:

A truth table with arguments and values:

Vector-valued Boolean expression:

A 2D truth table:

A 3D truth table:

Generate a truth table for a pure Boolean function:

Specify the position of arguments to use:

Position and grouping of arguments to use:

Expressions do not need to produce Boolean values:

Generalizations & Extensions (1)

Generate a truth table without explicitly giving a variable list:

The variables and ordering used are given by BooleanVariables:

Applications (3)

Compute the probability for an event as the ratio of true cases to total cases:

The probabilities for some events:

The probability that exactly three variables are true:

Show that

:

Assume that you pay 2 units when

and that you earn 1 unit when

:

The expected earning when it is equally probable that

are true or false:

The risk or variance is:

Generate the truth rules for a Boolean expression:

Use the rules to evolve a cellular automaton:

Properties & Relations (6)

A BooleanTable with n variables has

elements:

With n and m variables the resulting matrix has

values:

BooleanTable with several variable iterators evaluates the outermost iterator first:

An equivalent form:

BooleanTable enumerates values in the same order as Tuples[{True, False}, n]:

Three variables:

SatisfiabilityCount efficiently counts the number of True elements in BooleanTable:

In this case the BooleanTable would have

elements:

Give an enumerated BooleanFunction:

Compute its truth table:

The order of enumeration is consistent with FromDigits:

Use BooleanFunction to convert a truth table to a function or expression:

Convert to a Boolean function:

Use it as any other function:

Convert to a disjunctive normal form:

Convert to a "NAND" form:

Neat Examples (1)

The truth table for BooleanCountingFunction: