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Logical connectives. In 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}). [1] [2] Alternative names are switching function, used especially in older computer science literature, [3] [4] and truth function (or logical function), used in logic.
v. t. e. A 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. [1]
propositional logic, Boolean algebra, first-order logic. ⊥ {\displaystyle \bot } denotes a proposition that is always false. The symbol ⊥ may also refer to perpendicular lines. The proposition. ⊥ ∧ P {\displaystyle \bot \wedge P} is always false since at least one of the two is unconditionally false. ∀.
In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables are the truth values true and false, usually denoted 1 and 0, whereas in elementary algebra the values of the variables are numbers. Second, Boolean algebra uses logical operators such ...
Truth function. In logic, a truth function [1] is a function that accepts truth values as input and produces a unique truth value as output. In other words: the input and output of a truth function are all truth values; a truth function will always output exactly one truth value, and inputting the same truth value (s) will always output the ...
In logic, a symbol that represents a function from individuals or tuples of individuals to truth values, essentially a generalization of a predicate. predicate functor logic A logical system that combines elements of predicate logic with the concept of functors, allowing for a more expressive representation of properties and relations.
Logical connectives. In logic, mathematics and linguistics, and ( ) is the truth-functional operator of conjunction or logical conjunction. The logical connective of this operator is typically represented as [1] or or (prefix) or or [2] in which is the most modern and widely used. The and of a set of operands is true if and only if all of its ...
In Boolean logic, logical NOR, [1] non-disjunction, or joint denial [1] is a truth-functional operator which produces a result that is the negation of logical or. That is, a sentence of the form ( p NOR q) is true precisely when neither p nor q is true—i.e. when both p and q are false. It is logically equivalent to and , where the symbol ...