Normal Forms

Abstract

We now list some logical equivalences. Their proofs follow immediately from the definitions of the previous chapter. To facilitate the reading, outer parentheses are omitted throughout:

$$\begin{gathered} F \vee G \equiv G \vee F \hfill \\ \left( {F \vee G} \right) \vee H \equiv F \vee \left( {G \vee H} \right) \hfill \\ F \vee F \equiv F \hfill \\ \neg \neg F \equiv F \hfill \\ F \vee O \equiv F for each unsatisfiable formula O \hfill \\ F \vee \neg O \equiv \neg O for each unsatisfiable formula O \hfill \\ \neg \left( {\neg F \vee G} \right) \vee G \equiv \neg \left( {\neg G \vee F} \right) \vee F. \hfill \\ \end{gathered}$$