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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 ...
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). When it is necessary to clarify whether inclusive or exclusive or is intended, English speakers sometimes uses the phrase and/or.
Venn diagram for "A or B", with inclusive or (OR) Venn diagram for "A or B", with exclusive or (XOR) The fallacy lies in concluding that one disjunct must be false because the other disjunct is true; in fact they may both be true because "or" is defined inclusively rather than exclusively. It is a fallacy of equivocation between the operations ...
So by definition, x → y is true when x is false (relevance logic rejects this definition, by viewing an implication with a false premise as something other than either true or false). Exclusive OR (XOR) The second operation, x ⊕ y, or Jxy, is called exclusive or (often abbreviated as XOR) to distinguish it from disjunction as the inclusive ...
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 ...
Wherever logic is applied, especially in mathematical discussions, it has the same meaning as above: it is an abbreviation for if and only if, indicating that one statement is both necessary and sufficient for the other. This is an example of mathematical jargon (although, as noted above, if is more often used than iff in statements of definition).
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.
XOR gate (sometimes EOR, or EXOR and pronounced as Exclusive OR) is a digital logic gate that gives a true (1 or HIGH) output when the number of true inputs is odd. An XOR gate implements an exclusive or ( ↮ {\displaystyle \nleftrightarrow } ) from mathematical logic ; that is, a true output results if one, and only one, of the inputs to the ...