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Logic Terms

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Study guide for logic

An argument is valid if and only if, assuming the premises are true, the conclusion must be true. Validity guarantees the truth of the conclusion, assuming the premises are true.
An invalid argument is if the premises are true and the conclusion is false.
An argument is sound if and only if it is sound and all the premises are true.
A tautology is a sentence that is logically true in virtue of its truth-functional structure. This can be checked using truth tables since S is a tautology if and only if every row of the truth table for S assigns true to the main connective.
Tautological consequence: A sentence S is a tautological consequence of some premises if S follows from the premises simply in virtue of the meanings of the truth-functional connectives. We can check for tauto- logical consequence by means of truth tables, since S is a tautological consequence of the premises if and only if every row of their joint truth table that assigns true to each of premise also assigns true to S. All tautological consequences are logical consequences, but not all logical consequences are tautological consequences.
Tautological equivalence: Two sentences are tautologically equivalent if they are equivalent simply in virtue of the meanings of the truth-func- tional connectives. We can check for tautological equivalence by means of truth tables since two sentences Q and S are tautologically equivalent if and only if every row of their joint truth table assigns the same value to the main connectives of Q and S.
Counterexample: A counterexample to an argument is a possible situation in which all the premises of the argument are true but the conclusion is false. Finding even a single counterexample is sufficient to show that an argument is not logically valid.
Truth-functional connective: A sentence connective with the property that the truth-value

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