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Disjunction in natural languages does not precisely match the interpretation of in classical logic. Notably, classical disjunction is inclusive while natural language disjunction is often understood exclusively, as the following English example typically would be. [1] Mary is eating an apple or a pear.
The OR gate is a digital logic gate that implements logical disjunction. The OR gate outputs "true" if any of its inputs is "true"; otherwise it outputs "false". The input and output states are normally represented by different voltage levels.
The second example shows that the exclusive inference vanishes away under downward entailing contexts. If disjunction were understood as exclusive in this example, it would leave open the possibility that some people ate both rice and beans. [4] 2. Mary is either a singer or a poet or both. 3. Nobody ate either rice or beans.
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.
In boolean logic, a disjunctive normal form (DNF) is a canonical normal form of a logical formula consisting of a disjunction of conjunctions; it can also be described as an OR of ANDs, a sum of products, or — in philosophical logic — a cluster concept. [1] As a normal form, it is useful in automated theorem proving.
Related puzzles involving disjunction include free choice inferences, Hurford's Constraint, and the contribution of disjunction in alternative questions. Other apparent discrepancies between natural language and classical logic include the paradoxes of material implication , donkey anaphora and the problem of counterfactual conditionals .
Venn diagram of . 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.
A logic gate is a device that performs a Boolean function, a logical operation performed on one or more binary inputs that produces a single binary output. Depending on the context, the term may refer to an ideal logic gate, one that has, for instance, zero rise time and unlimited fan-out, or it may refer to a non-ideal physical device [1] (see ...