Lemma: Construction of Conjunctive and Disjunctive Canonical Normal Forms

Let $\phi$ be a proposition with the corresponding Boolean function $f_\phi.$ Then there exist either the disjunctive or the conjunctive canonical (or both) normal forms $\operatorname{dcnf}(\phi)$ and $\operatorname{ccnf}(\phi)$ with the same Boolean functions:


If $\operatorname{dcnf}(\phi)$ and/or $\operatorname{ccnf}(\phi)$ exist, then they are unique except of the order of literals and the minterms respectively maxterms.

Proofs: 1 Corollaries: 1

Proofs: 1

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  1. Mendelson Elliott: "Theory and Problems of Boolean Algebra and Switching Circuits", McGraw-Hill Book Company, 1982
  2. Hoffmann, Dirk: "Theoretische Informatik, 3. Auflage", Hanser, 2015