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where denotes OR, denotes AND, and denotes NOT (Mendelson 1997, p. 30).
Every statement in logic consisting of a combination of multiple , , and s can be written in conjunctive normal form.
An expression can be put in conjunctive normal form using the Wolfram Language using the following code:
ConjunctiveNormalForm[f_] :=
Not[LogicalExpand[Not[f]]] //. {
Not[a_Or] :> And @@ (Not /@ List @@ a),
Not[a_And] :> Or @@ (Not /@ List @@ a)
}
Mendelson, E. Introduction to Mathematical Logic, 4th ed. London: Chapman & Hall, p. 30, 1997.
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