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= $\[\mathrm{x1},...,\mathrm{xn}\]$, where $\mathrm{x1},...,\mathrm{xn}$, are identifiers in the expression, then $T\[\mathrm{v1},...,\mathrm{vn}\]$ 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.

$\mathrm{with}\left(\mathrm{Logic}\right)\:$

$\mathrm{T1}≔\mathrm{TruthTable}\left(a\&xorb\right)$

$\mathrm{T1}≔\left[\begin{array}{cccc}& a& b& \mathrm{value}\\ 1& \mathrm{false}& \mathrm{false}& \mathrm{false}\\ 2& \mathrm{false}& \mathrm{true}& \mathrm{true}\\ 3& \mathrm{true}& \mathrm{false}& \mathrm{true}\\ 4& \mathrm{true}& \mathrm{true}& \mathrm{false}\end{array}\right]$

$\mathrm{TruthTable}\left(a\&xorb\,\mathrm{output}=\mathrm{Matrix}\right)$

$\left[\begin{array}{ccc}\mathrm{false}& \mathrm{false}& \mathrm{false}\\ \mathrm{false}& \mathrm{true}& \mathrm{true}\\ \mathrm{true}& \mathrm{false}& \mathrm{true}\\ \mathrm{true}& \mathrm{true}& \mathrm{false}\end{array}\right]$

$\mathrm{TruthTable}\left(a\&xorb\,\mathrm{output}=\mathrm{table}\right)$

$table\left(\left[\left(\mathrm{true}\,\mathrm{true}\right)=\mathrm{false}\,\left(\mathrm{true}\,\mathrm{false}\right)=\mathrm{true}\,\left(\mathrm{false}\,\mathrm{false}\right)=\mathrm{false}\,\left(\mathrm{false}\,\mathrm{true}\right)=\mathrm{true}\right]\right)$

$\mathrm{T2}≔\mathrm{TruthTable}\left(\left(\left(\&not\left(a\right)\right)\&norb\right)\&iffc\,\left[a\,b\,c\right]\,\mathrm{output}=\mathrm{table}\right)\:$

$\mathrm{T2}\left[\mathrm{true},\mathrm{false},\mathrm{false}\right]$

$\mathrm{false}$

$\mathrm{T3}≔\mathrm{TruthTable}\left(a\&xorb\,\left[a\,b\right]\,\mathrm{form}=\mathrm{MOD2}\,\mathrm{output}=\mathrm{table}\right)\:$

$\mathrm{T3}\left[1,0\right]$

$1$

The Logic[TruthTable] command was updated in Maple 2016.