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  2. Negation - Wikipedia

    en.wikipedia.org/wiki/Negation

    As a further example, negation can be defined in terms of NAND and can also be defined in terms of NOR. Algebraically, classical negation corresponds to complementation in a Boolean algebra, and intuitionistic negation to pseudocomplementation in a Heyting algebra. These algebras provide a semantics for classical and intuitionistic logic.

  3. Literal (mathematical logic) - Wikipedia

    en.wikipedia.org/wiki/Literal_(mathematical_logic)

    A negative literal is the negation of an atom (e.g., ). The polarity of a literal is positive or negative depending on whether it is a positive or negative literal. In logics with double negation elimination (where ¬ ¬ x ≡ x {\displaystyle \lnot \lnot x\equiv x} ) the complementary literal or complement of a literal l {\displaystyle l} can ...

  4. Logical connective - Wikipedia

    en.wikipedia.org/wiki/Logical_connective

    A less trivial example of a redundancy is the classical equivalence between and . Therefore, a classical-based logical system does not need the conditional operator " → {\displaystyle \to } " if " ¬ {\displaystyle \neg } " (not) and " ∨ {\displaystyle \vee } " (or) are already in use, or may use the " → {\displaystyle \to } " only as a ...

  5. Involution (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Involution_(mathematics)

    Any involution is a bijection.. The identity map is a trivial example of an involution. Examples of nontrivial involutions include negation (x ↦ −x), reciprocation (x ↦ 1/x), and complex conjugation (z ↦ z) in arithmetic; reflection, half-turn rotation, and circle inversion in geometry; complementation in set theory; and reciprocal ciphers such as the ROT13 transformation and the ...

  6. Double negation - Wikipedia

    en.wikipedia.org/wiki/Double_negation

    In propositional logic, the double negation of a statement states that "it is not the case that the statement is not true". In classical logic, every statement is logically equivalent to its double negation, but this is not true in intuitionistic logic; this can be expressed by the formula A ≡ ~(~A) where the sign ≡ expresses logical equivalence and the sign ~ expresses negation.

  7. List of logic symbols - Wikipedia

    en.wikipedia.org/wiki/List_of_logic_symbols

    The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics. Additionally, the subsequent columns contains an informal explanation, a short example, the Unicode location, the name for use in HTML documents, [1] and the LaTeX symbol.

  8. Negative number - Wikipedia

    en.wikipedia.org/wiki/Negative_number

    This thermometer is indicating a negative Fahrenheit temperature (−4 °F). In mathematics, a negative number is the opposite of a positive real number. [1] Equivalently, a negative number is a real number that is less than zero. Negative numbers are often used to represent the magnitude of a loss or deficiency.

  9. Contraposition - Wikipedia

    en.wikipedia.org/wiki/Contraposition

    The negation is "There is at least one quadrilateral that does not have four sides. " This statement is clearly false. Since the statement and the converse are both true, it is called a biconditional , and can be expressed as " A polygon is a quadrilateral if, and only if, it has four sides.