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  2. Necessity and sufficiency - Wikipedia

    en.wikipedia.org/wiki/Necessity_and_sufficiency

    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". [9] [1] By contraposition, this is the same thing as "whenever P is true, so is Q". The logical relation between P and Q is expressed as "if P, then Q" and denoted "P ⇒ Q" (P implies Q).

  3. List of logic symbols - Wikipedia

    en.wikipedia.org/wiki/List_of_logic_symbols

    Corner quotes, also called “Quine quotes”; for quasi-quotation, i.e. quoting specific context of unspecified (“variable”) expressions; [3] also used for denoting Gödel number; [4] for example “⌜G⌝” denotes the Gödel number of G. (Typographical note: although the quotes appears as a “pair” in unicode (231C and 231D), they ...

  4. 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 ...

  5. Two envelopes problem - Wikipedia

    en.wikipedia.org/wiki/Two_envelopes_problem

    In non-technical language, what goes wrong (see Necktie paradox) is that, in the scenario provided, the mathematics use relative values of A and B (that is, it assumes that one would gain more money if A is less than B than one would lose if the opposite were true). However, the two values of money are fixed (one envelope contains, say, $20 and ...

  6. Mathematical fallacy - Wikipedia

    en.wikipedia.org/wiki/Mathematical_fallacy

    In mathematics, certain kinds of mistaken proof are often exhibited, and sometimes collected, as illustrations of a concept called mathematical fallacy.There is a distinction between a simple mistake and a mathematical fallacy in a proof, in that a mistake in a proof leads to an invalid proof while in the best-known examples of mathematical fallacies there is some element of concealment or ...

  7. AOL

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    The search engine that helps you find exactly what you're looking for. Find the most relevant information, video, images, and answers from all across the Web.

  8. Trump aims to deport all immigrants in the US illegally - AOL

    www.aol.com/news/trump-says-aims-deport...

    The pro-immigration American Immigration Council estimated that deporting all immigrants in the U.S. illegally over more than a decade would cost $88 billion annually. Homan said the minimum ...

  9. Your Call: When do you gamble on a fake punt? - AOL

    www.aol.com/sports/call-gamble-fake-punt...

    Jim Harbaugh's gamble in his own territory didn't pay off, but his defense bailed him out.