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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.
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.
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:
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:
A way of expressing a logical formula as a conjunction of clauses, where each clause is a disjunction of literals. connected A property of a graph in which there is a path between any two vertices, or a property of a topological space in which it cannot be divided into two disjoint nonempty open sets. connexive logic
Intermediate logics are in between intuitionistic logic and classical logic. Here are a few intermediate logics: Jankov logic (KC) is an extension of intuitionistic logic, which can be axiomatized by the intuitionistic axiom system plus the axiom [13].