Dual - Maple Help

Logic

 Dual
 construct the dual of a Boolean expression

 Calling Sequence Dual(b)

Parameters

 b - Boolean expression

Description

 • The Dual command returns the dual of the Boolean expression b, that is, the expression generated by replacing &and with &or, &or with &and, leaving ¬ fixed, and extending to the remaining Boolean operators by their formulas in terms of &and, &or, and ¬.

Examples

 > $\mathrm{with}\left(\mathrm{Logic}\right):$
 > $\mathrm{Dual}\left(a\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}&and\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\left(¬\left(a\right)\right)=\mathrm{false}\right)$
 ${a}{\vee }\left({¬}{a}\right){=}{\mathrm{true}}$ (1)
 > $\mathrm{Dual}\left(a\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}&implies\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}b\right)$
 ${¬}\left({b}{⇒}{a}\right)$ (2)
 > $\mathrm{Dual}\left(\left(\left(¬\left(a\right)\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}&nor\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}b\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}&iff\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}c\right)$
 $\left(\left({¬}{a}\right){↑}{b}\right){⊻}{c}$ (3)