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  2. Quantifier (logic) - Wikipedia

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

    Peirce's notation can be found in the writings of Ernst Schröder, Leopold Loewenheim, Thoralf Skolem, and Polish logicians into the 1950s. Most notably, it is the notation of Kurt Gödel's landmark 1930 paper on the completeness of first-order logic, and 1931 paper on the incompleteness of Peano arithmetic.

  3. List of logic symbols - Wikipedia

    en.wikipedia.org/wiki/List_of_logic_symbols

    This is a statement in the metalanguage, not the object language. The notation a ≡ b {\displaystyle a\equiv b} may occasionally be seen in physics, meaning the same as a := b {\displaystyle a:=b} .

  4. Existential quantification - Wikipedia

    en.wikipedia.org/wiki/Existential_quantification

    This is a single statement using existential quantification. It is roughly analogous to the informal sentence "Either 0 × 0 = 25 {\displaystyle 0\times 0=25} , or 1 × 1 = 25 {\displaystyle 1\times 1=25} , or 2 × 2 = 25 {\displaystyle 2\times 2=25} , or... and so on," but more precise, because it doesn't need us to infer the meaning of the ...

  5. Contraposition - Wikipedia

    en.wikipedia.org/wiki/Contraposition

    This statement is true because it is a restatement of a definition. The contrapositive of this statement is "If cannot be expressed as an irreducible fraction, then it is not rational". This contrapositive, like the original statement, is also true.

  6. Propositional calculus - Wikipedia

    en.wikipedia.org/wiki/Propositional_calculus

    It is also called propositional logic, [2] statement logic, [1] sentential calculus, [3] sentential logic, [4] [1] or sometimes zeroth-order logic. [ b ] [ 6 ] [ 7 ] [ 8 ] Sometimes, it is called first-order propositional logic [ 9 ] to contrast it with System F , but it should not be confused with first-order logic .

  7. Disjunctive syllogism - Wikipedia

    en.wikipedia.org/wiki/Disjunctive_syllogism

    In classical logic, disjunctive syllogism [1] [2] (historically known as modus tollendo ponens (MTP), [3] Latin for "mode that affirms by denying") [4] is a valid argument form which is a syllogism having a disjunctive statement for one of its premises. [5] [6] An example in English: I will choose soup or I will choose salad. I will not choose ...

  8. Discrete mathematics - Wikipedia

    en.wikipedia.org/wiki/Discrete_mathematics

    Concepts and notations from discrete mathematics are useful in studying and describing objects and problems in branches of computer science, such as computer algorithms, programming languages, cryptography, automated theorem proving, and software development. Conversely, computer implementations are significant in applying ideas from discrete ...

  9. De Morgan's laws - Wikipedia

    en.wikipedia.org/wiki/De_Morgan's_laws

    De Morgan's laws represented with Venn diagrams.In each case, the resultant set is the set of all points in any shade of blue. In propositional logic and Boolean algebra, De Morgan's laws, [1] [2] [3] also known as De Morgan's theorem, [4] are a pair of transformation rules that are both valid rules of inference.

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