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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 ...
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.
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.
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.
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:
A symbol or word used in logic to connect propositions or sentences, forming more complex expressions that convey relationships such as conjunction, disjunction, and negation. logical consequence A relationship between statements where the truth of one or more premises necessitates the truth of a conclusion, based on the logical structure of ...
The AND gate is a basic digital logic gate that implements the logical conjunction (∧) from mathematical logic – AND gates behave according to their truth table. A HIGH output (1) results only if all the inputs to the AND gate are HIGH (1). If all of the inputs to the AND gate are not HIGH, a LOW (0) is outputted.
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 .