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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 ∧ {\displaystyle \wedge } [ 1 ] or & {\displaystyle \&} or K {\displaystyle K} (prefix) or × {\displaystyle \times } or ⋅ {\displaystyle \cdot } [ 2 ] in ...
Each logic operator can be used in an assertion about variables and operations, showing a basic rule of inference. Examples: The column-14 operator (OR), shows Addition rule : when p =T (the hypothesis selects the first two lines of the table), we see (at column-14) that p ∨ q =T.
In logic, a set of symbols is commonly used to express logical representation. The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics.
Both conjunction and disjunction are associative, commutative and idempotent in classical logic, most varieties of many-valued logic and intuitionistic logic. The same is true about distributivity of conjunction over disjunction and disjunction over conjunction, as well as for the absorption law.
In propositional logic and Boolean algebra, there is a duality between conjunction and disjunction, [1] [2] [3] also called the duality principle. [4] [5] [6] It is the most widely known example of duality in logic. [1] The duality consists in these metalogical theorems:
Logical conjunction is an operation on two logical values, typically the values of two propositions, that produces a value of true if both of its operands are true. The truth table for p AND q (also written as p ∧ q , Kpq , p & q , or p ⋅ {\displaystyle \cdot } q ) is as follows:
Conjunction introduction (often abbreviated simply as conjunction and also called and introduction or adjunction) [1] [2] [3] is a valid rule of inference of propositional logic. The rule makes it possible to introduce a conjunction into a logical proof .
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 same truth value.