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Discrete mathematics

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Some people use "tautology" in logic in a wide sense, to mean any logically true wff.

But others use "tautology" more narrowly to mean true in virtue of truth-functional structure (so, "valid by the truth-table test").

So, for example, ∀xFx→Fa∀xFx→Fa would count as a tautology in the first, wide, sense but not in the second, narrow, sense.

How to use 'tautology', then, this is a matter of terminological preference, I think.

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