Complement returns the complement of a Boolean expression, that is, the expression generated by replacing &and with &or, &or with &and, negating all variable instances, and extending to the remaining Boolean operators by their formulas in terms of &and, &or, and &not.

For an input b, the resulting expression will be equivalent to not b in truth value.

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

$\mathrm{Complement}\left(a\&and\left(\&not\left(a\right)\right)=\mathrm{false}\right)$

$\left(\neg a\right)\vee a=\mathrm{true}$

$\mathrm{Complement}\left(a\&impliesb\right)$

$\neg \left(\left(\neg b\right)\Rightarrow \left(\neg a\right)\right)$

$\mathrm{Complement}\left(\left(\left(\&not\left(a\right)\right)\&norb\right)\&iffc\right)$

$\left(a\uparrow \left(\neg b\right)\right)⊻\left(\neg c\right)$

The Logic[Complement] command was introduced in Maple 2016.

For more information on Maple 2016 changes, see Updates in Maple 2016.