Logic
TruthTable
construct the truth table of a Boolean expression
Calling Sequence
Parameters
Description
Examples
Compatibility
TruthTable(expr, L, opt)
expr
-
Boolean expression
L
(optional) list of identifiers appearing in the expression
opt
(optional) equation(s) of the form option=value, where option is one of 'output' or 'form'; specify options for the TruthTable command
TruthTable(expr) returns the truth table corresponding to the Boolean expression expr.
The optional parameter L, which can only be used with output=table, specifies a list of identifiers appearing in the expression. This list determines the ordering used for table indices. That is, if T is the table returned and L= [x1,...,xn], where x1,...,xn, are identifiers in the expression, then T[v1,...,vn] is equivalent to eval( expr, [x1=v1, ..., xn=vn] ).
If L is omitted, the identifiers appearing in the expression are listed in the resulting truth table in lexicographical order.
The optional parameter output=returnform specifies the form of the returned truth table: table, Matrix, or 'DataFrame'. The default is 'DataFrame'.
The optional parameter form=tblform specifies the type of the inputs and output; by default, this is boolean. If form=MOD2 is specified, then the indices and entries will be zeroes and ones.
with(Logic):
T1 := TruthTable(a &xor b);
T1≔abvalue1falsefalsefalse2falsetruetrue3truefalsetrue4truetruefalse
TruthTable(a &xor b, output=Matrix);
falsefalsefalsefalsetruetruetruefalsetruetruetruefalse
TruthTable(a &xor b, output=table);
table⁡true,false=true,true,true=false,false,true=true,false,false=false
T2 := TruthTable((¬ a) &nor b &iff c, [a,b,c], output=table):
T2[true, false, false];
false
T3 := TruthTable(a &xor b, [a,b], form=MOD2, output=table):
T3[1, 0];
1
The Logic[TruthTable] command was updated in Maple 2016.
See Also
Logic/Satisfy
type[tabular]
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