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[Solved]: definition of formula validity

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I read in some sources that valid formulas are tautologies (valid under every evaluation). In the others, I read that these are formulas that have conclusions true when premises are true. Are these just equivalent definitions because ⊨ P → Q is equivalent to P ⊨ Q?

Asked By : Val

Answered By : Dave Clarke

Yes. These definitions are equivalent, noting that not all valid formula have the form $P\to Q$, though any formula $Q$ is equivalent to $\top\to Q$.

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