The BooleanSimplify command returns a minimal sum of products expansion of the given Boolean expression.

The expression returned is a minimal (irreducible) sum of prime implicants.

Note: BooleanSimplify does not guarantee that the returned expansion is a minimum sum of prime implicants.

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

$\mathrm{BooleanSimplify}\left(a\&or\left(a\&andb\right)\right)$

$a$

$\mathrm{BooleanSimplify}\left(\left(a\&andb\right)\&or\left(a\&and\left(\&not\left(b\right)\right)\right)\right)$

$a$

$\mathrm{BooleanSimplify}\left(a\&iff\left(a\&orb\right)\right)$

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

$\mathrm{BooleanSimplify}\left(\mathrm{`\&or`}\left(a\&andb\,\left(\&not\left(a\right)\right)\&andc\,b\&andc\right)\right)$

$\left(a\wedge b\right)\vee \left(c\wedge \left(\neg a\right)\right)$