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Logic

 BooleanSimplify
 simplify Boolean expression

 Calling Sequence BooleanSimplify(b)

Parameters

 b - Boolean expression

Description

 • 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.

Examples

 > $\mathrm{with}\left(\mathrm{Logic}\right):$
 > $\mathrm{BooleanSimplify}\left(a\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}&or\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\left(a\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}&and\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}b\right)\right)$
 ${a}$ (1)
 > $\mathrm{BooleanSimplify}\left(\left(a\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}&and\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}b\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}&or\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\left(a\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}&and\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\left(¬\left(b\right)\right)\right)\right)$
 ${a}$ (2)
 > $\mathrm{BooleanSimplify}\left(a\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}&iff\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}\left(a\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}&or\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}b\right)\right)$
 ${a}{\vee }\left({¬}{b}\right)$ (3)
 > $\mathrm{BooleanSimplify}\left(\mathrm{&or}\left(a\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}&and\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}b,\left(¬\left(a\right)\right)\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}&and\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}c,b\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}&and\phantom{\rule[-0.0ex]{0.3em}{0.0ex}}c\right)\right)$
 $\left({a}{\wedge }{b}\right){\vee }\left({c}{\wedge }\left({¬}{a}\right)\right)$ (4)