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Exclusive or, exclusive disjunction, exclusive alternation, logical non-equivalence, or logical inequality is a logical operator whose negation is the logical biconditional. With two inputs, XOR is true if and only if the inputs differ (one is true, one is false). With multiple inputs, XOR is true if and only if the number of true inputs is odd ...
Because the logical or means a disjunction formula is true when either one or both of its parts are true, it is referred to as an inclusive disjunction. This is in contrast with an exclusive disjunction, which is true when one or the other of the arguments are true, but not both (referred to as exclusive or, or XOR).
In linguistics, clusivity [1] is a grammatical distinction between inclusive and exclusive first-person pronouns and verbal morphology, also called inclusive "we" and exclusive "we". Inclusive "we" specifically includes the addressee, while exclusive "we" specifically excludes the addressee; in other words, two (or more) words that both ...
In logic, two propositions and are mutually exclusive if it is not logically possible for them to be true at the same time; that is, () is a tautology. To say that more than two propositions are mutually exclusive, depending on the context, means either 1. "() () is a tautology" (it is not logically possible for more than one proposition to be true) or 2. "() is a tautology" (it is not ...
A definition that refers to a set that includes the entity being defined, often leading to paradoxes in naive set theories. inclusive disjunction A logical operation that returns true if at least one of its operands is true; corresponds to the logical OR. inclusive first-order logic
References on English usage strongly criticize the phrase as "ugly" [2] and "Janus-faced". [4] William Strunk, Jr., and E.B. White, in their classic The Elements of Style–recognized by Time one of the 100 best and most influential non-fiction books written in English since 1923, [6] say and/or is "A device, or shortcut, that damages a sentence and often leads to confusion or ambiguity". [3]
All other logic gates may be made from these three gates; any function in binary mathematics may be implemented with them. [3] It is sometimes called the inclusive OR gate to distinguish it from XOR, the exclusive OR gate. [4] The behavior of OR is the same as XOR except in the case of a 1 for both inputs.
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.