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  2. Validity (logic) - Wikipedia

    en.wikipedia.org/wiki/Validity_(logic)

    A statement can be called valid, i.e. logical truth, in some systems of logic like in Modal logic if the statement is true in all interpretations. In Aristotelian logic statements are not valid per se. Validity refers to entire arguments. The same is true in propositional logic (statements can be true or false but not called valid or invalid).

  3. Logical truth - Wikipedia

    en.wikipedia.org/wiki/Logical_truth

    A statement is logically true if, and only if its opposite is logically false. The opposite statements must contradict one another. In this way all logical connectives can be expressed in terms of preserving logical truth. The logical form of a sentence is determined by its semantic or syntactic structure and by the placement of logical constants.

  4. Proof by contradiction - Wikipedia

    en.wikipedia.org/wiki/Proof_by_contradiction

    In logic, proof by contradiction is a form of proof that establishes the truth or the validity of a proposition by showing that assuming the proposition to be false leads to a contradiction. Although it is quite freely used in mathematical proofs, not every school of mathematical thought accepts this kind of nonconstructive proof as universally ...

  5. Contraposition - Wikipedia

    en.wikipedia.org/wiki/Contraposition

    If a statement's inverse is false, then its converse is false (and vice versa). If a statement's negation is false, then the statement is true (and vice versa). If a statement (or its contrapositive) and the inverse (or the converse) are both true or both false, then it is known as a logical biconditional.

  6. Proof by example - Wikipedia

    en.wikipedia.org/wiki/Proof_by_example

    In logic and mathematics, proof by example (sometimes known as inappropriate generalization) is a logical fallacy whereby the validity of a statement is illustrated through one or more examples or cases—rather than a full-fledged proof. [1] [2] The structure, argument form and formal form of a proof by example generally proceeds as follows ...

  7. Propositional calculus - Wikipedia

    en.wikipedia.org/wiki/Propositional_calculus

    Valid formula (tautology): A sentence ... it is possible to prove a formula's validity by using a truth table, ... p and not p is false, is a true statement

  8. Vacuous truth - Wikipedia

    en.wikipedia.org/wiki/Vacuous_truth

    These examples, one from mathematics and one from natural language, illustrate the concept of vacuous truths: "For any integer x, if x > 5 then x > 3." [11] – This statement is true non-vacuously (since some integers are indeed greater than 5), but some of its implications are only vacuously true: for example, when x is the integer 2, the statement implies the vacuous truth that "if 2 > 5 ...

  9. Modus tollens - Wikipedia

    en.wikipedia.org/wiki/Modus_tollens

    This is a valid argument since it is not possible for the conclusion to be false if the premises are true. (It is conceivable that there may have been an intruder that the dog did not detect, but that does not invalidate the argument; the first premise is "if the dog detects an intruder".