Example 13 is a tautology. This is an example of De Morgan’s laws.
Example 14 is a tautology.
Definition 19 A formula is satisfiable iff there is some valuation such that Otherwise, we say that is contradictory, or unsatisfiable.
Remark 7 is unsatisfiable iff is a tautology.
Example 15 is not a tautology, but it is satisfiable.
Definition 20 If is a valuation and is a set of formulas, iff for all For a given if there is such a valuation we say that is satisfiable, or has a model, and that is a model of Otherwise, is unsatisfiable or contradictory.