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 &not fixed, and extending to the remaining Boolean operators by their formulas in terms of &and, &or, and &not.

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

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

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

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

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

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

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