◀ ▲ ▶Branches / Logic / Lemma: Construction of Conjunctive and Disjunctive Canonical Normal Forms

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:

$$f_\phi=f_{\operatorname{dcnf}(\phi)}=f_{\operatorname{ccnf}(\phi)}.$$

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.

Table of Contents

Proofs: 1 Corollaries: 1

Mentioned in:

Proofs: 1

Thank you to the contributors under CC BY-SA 4.0!

Github:

References

Bibliography

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