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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.

with(Logic):

BooleanSimplify(a &or (a &and b));

$a$

BooleanSimplify((a &and b) &or (a &and (&not b)));

$a$

BooleanSimplify(a &iff (a &or b));

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

BooleanSimplify(&or(a &and b, (&not a) &and c, b &and c));

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