Definition:Semantic Equivalence/Boolean Interpretations/Definition 3
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Definition
Let $\mathbf A, \mathbf B$ be WFFs of propositional logic.
Then $\mathbf A$ and $\mathbf B$ are equivalent for boolean interpretations if and only if:
- $\mathbf A \iff \mathbf B$ is a tautology
where $\iff$ is the biconditional connective.
Also see
Sources
- 1988: Alan G. Hamilton: Logic for Mathematicians (2nd ed.) ... (previous) ... (next): $\S 1$: Informal statement calculus: $\S 1.2$: Truth functions and truth tables: Definition $1.7$
- 1996: H. Jerome Keisler and Joel Robbin: Mathematical Logic and Computability ... (previous) ... (next): $\S 1.14$: Exercise $15$