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  2. Necessity and sufficiency - Wikipedia

    en.wikipedia.org/wiki/Necessity_and_sufficiency

    The sun being above the horizon is a necessary condition for direct sunlight; but it is not a sufficient condition, as something else may be casting a shadow, e.g., the moon in the case of an eclipse. The assertion that Q is necessary for P is colloquially equivalent to "P cannot be true unless Q is true" or "if Q is false, then P is false".

  3. Material implication (rule of inference) - Wikipedia

    en.wikipedia.org/wiki/Material_implication_(rule...

    Then if is true, that rules out the first disjunct, so we have . In short, P → Q {\displaystyle P\to Q} . [ 3 ] However, if P {\displaystyle P} is false, then this entailment fails, because the first disjunct ¬ P {\displaystyle \neg P} is true, which puts no constraint on the second disjunct Q {\displaystyle Q} .

  4. 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.

  5. Truth table - Wikipedia

    en.wikipedia.org/wiki/Truth_table

    In ordinary language terms, if both p and q are true, then the conjunction p ∧ q is true. For all other assignments of logical values to p and to q the conjunction p ∧ q is false. It can also be said that if p, then p ∧ q is q, otherwise p ∧ q is p.

  6. Proof by contradiction - Wikipedia

    en.wikipedia.org/wiki/Proof_by_contradiction

    The proposition to be proved is P. We assume P to be false, i.e., we assume ¬P. It is then shown that ¬P implies falsehood. This is typically accomplished by deriving two mutually contradictory assertions, Q and ¬Q, and appealing to the law of noncontradiction. Since assuming P to be false leads to a contradiction, it is concluded that P is ...

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  8. Implicational propositional calculus - Wikipedia

    en.wikipedia.org/wiki/Implicational...

    Implication alone is not functionally complete as a logical operator because one cannot form all other two-valued truth functions from it.. For example, the two-place truth function that always returns false is not definable from → and arbitrary propositional variables: any formula constructed from → and propositional variables must receive the value true when all of its variables are ...

  9. Are False Positive Covid Tests Common? Doctors Explain. - AOL

    www.aol.com/false-positive-covid-tests-common...

    A false positive Covid-19 test result can happen, but it’s rare, says Brian Labus, Ph.D., M.P.H., assistant professor at the University of Nevada Las Vegas School of Public Health.