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# 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.
• The possible combinations of variable values are given in the order Tuples[{True, False}, n].
• 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[expr, vars1, ..., varss] is equivalent to Fold[BooleanTable, expr, {varss, ..., vars1}].
• 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.
The vector of truth values for Or:
Convert to 1, 0 form:
2D truth table for Or:
The vector of truth values for Or:
 Out[1]=
Convert to 1, 0 form:
 Out[2]=

2D truth table for Or:
 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:
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 x, y, z 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:
A BooleanTable with n variables has 2n elements:
With n and m variables the resulting matrix has 2n+m 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 21000 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:
The truth table for BooleanCountingFunction:
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