Boolean functionRelated conceptsPropositional calculusPredicate logicBoolean algebraTruth tableTruth functionBoolean functionFunctional completenessScope (logic) ApplicationsDigital logicProgramming languagesMathematical logicPhilosophy of logicIn mathematics, a Boolean function is a function whose arguments and result assume values from a two-element set (usually {true, false}, {0,1} or {−1,1}).
Logical connectiveIn logic, a logical connective (also called a logical operator, sentential connective, or sentential operator) is an operator that combines or modifies one or more logical variables or formulas, similarly to how arithmetic connectives like + {\displaystyle +} and − {\displaystyle -} combine or negate arithmetic expressions.
NegationIn logic, negation, also called the logical not or logical complement, is an operation that takes a proposition P {\displaystyle P} to another proposition "not P {\displaystyle P} ", written ¬ P {\displaystyle \neg P} , ∼ P {\displaystyle {\mathord {\sim }}P} , P ′ {\displaystyle P^{\prime }} or P ¯ {\displaystyle {\overline {P}}} . It is interpreted intuitively as being true when P {\displaystyle P} is false, and false when P {\displaystyle P} is true.
Logical NORRelated conceptsPropositional calculusPredicate logicBoolean algebraTruth tableTruth functionBoolean functionFunctional completenessScope (logic) ApplicationsDigital logicProgramming languagesMathematical logicPhilosophy of logicIn Boolean logic, logical NOR,non-disjunction, or joint denial is a truth-functional operator which produces a result that is the negation of logical or.
Sheffer strokeRelated conceptsPropositional calculusPredicate logicBoolean algebraTruth tableTruth functionBoolean functionFunctional completenessScope (logic) ApplicationsDigital logicProgramming languagesMathematical logicPhilosophy of logicIn Boolean functions and propositional calculus, the Sheffer stroke denotes a logical operation that is equivalent to the negation of the conjunction operation, expressed in ordinary language as "not both".
Truth tableRelated conceptsPropositional calculusPredicate logicBoolean algebraTruth tableTruth functionBoolean functionFunctional completenessScope (logic) ApplicationsDigital logicProgramming languagesMathematical logicPhilosophy of logicA truth table is a mathematical table used in logic—specifically in connection with Boolean algebra, Boolean functions, and propositional calculus—which sets out the functional values of logical expressions on each of their functional arguments, that is, for each combination of values taken by their logical variables.
Logical disjunctionRelated conceptsPropositional calculusPredicate logicBoolean algebraTruth tableTruth functionBoolean functionFunctional completenessScope (logic) ApplicationsDigital logicProgramming languagesMathematical logicPhilosophy of logicIn logic, disjunction (also known as logical disjunction, logical or, logical addition, or inclusive disjunction) is a logical connective typically notated as ∨ and read aloud as "or".
Logical conjunctionRelated conceptsPropositional calculusPredicate logicBoolean algebraTruth tableTruth functionBoolean functionFunctional completenessScope (logic) ApplicationsDigital logicProgramming languagesMathematical logicPhilosophy of logicIn logic, mathematics and linguistics, and (∧{\displaystyle \wedge }) is the truth-functional operator of conjunction or logical conjunction.Boolean expressionIn computer science, a Boolean expression (also known as logical expression) is an expression used in programming languages that produces a Boolean value when evaluated. A Boolean value is either true or false. A Boolean expression may be composed of a combination of the Boolean constants True/False or Yes/No, Boolean-typed variables, Boolean-valued operators, and Boolean-valued functions.
Mathematical logicMathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory). Research in mathematical logic commonly addresses the mathematical properties of formal systems of logic such as their expressive or deductive power. However, it can also include usage of logic to characterize correct mathematical reasoning or to establish foundations of mathematics.
Singleton (mathematics)In mathematics, a singleton (also known as a unit set or one-point set) is a set with exactly oneelement. For example, the set {0}{\displaystyle \{0\}} is a singleton whose single element is 0{\displaystyle 0}. PropertiesWithin the framework of Zermelo–Fraenkel set theory, the axiom of regularity guarantees that no set is an element of itself.
Set (mathematics)In mathematics, a set is a collection of different things; the things are called elements or members of the set and are typically mathematical objects: numbers, symbols, points in space, lines, other geometric shapes, variables, functions, or even other sets. Mathematics typically does not define precisely what constitutes a "set" or "collection", because such a definition would have to be in terms of something else previously defined.*As an Amazon Associate I earn from qualifying purchases.