Біреуі ғана ақиқат, екеуі емес: Логикалық амал

True when either but not both inputs are true

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. It gains the name "exclusive or" because the meaning of "or" is ambiguous when both operands are true. XOR excludes that case. Some informal ways of describing XOR are "one or the other but not both", "either one or the other", and "A or B, but not A and B". It is symbolized by the prefix operator and by the infix operators XOR (,/ɛ//k//s// /'/ɔ://r/, ,/ɛ//k//s// /'/ɔ:/, /'//k//s//ɔ://r/ or /'//k//s//ɔ:/), EOR, EXOR, , , , ⩛, , , and .

Disjunction is often understood exclusively in natural languages. In English, the disjunctive word "or" is often understood exclusively, particularly when used with the particle "either". The English example below would normally be understood in conversation as implying that Mary is not both a singer and a poet. 1. Mary is a singer or a poet. However, disjunction can also be understood inclusively, even in combination with "either". For instance, the first example below shows that "either" can be felicitously used in combination with an outright statement that both disjuncts are true. 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. Although Boole used mainly on classes, he also considered the case that are propositions in , and at the time is a connective. Furthermore, Boole used it exclusively. Although such use does not show the relationship between inclusive disjunction (for which is almost fixedly used nowadays) and exclusive disjunction, and may also bring about confusions with its other uses, some classical and modern textbooks still keep such use. was used by Christine Ladd Franklin in 1883. Strictly speaking, Ladd used to express " is not " or "No is ", i. e., used as exclusions, while implicitly has the meaning of exclusive disjunction since the article is titled as "On the Algebra of Logic". , denoting the negation of equivalence, was used by Ernst Schröder in 1890, Although the usage of as equivalence could be dated back to George Boole in 1847, Note that the Latin word "aut" means "exclusive or" and "vel" means "inclusive or", and that Peano use as inclusive disjunction. was used by Izrail Solomonovich Gradshtein (Израиль Соломонович Градштейн) in 1936.
was used by Claude Shannon in 1938. Shannon borrowed the symbol as exclusive disjunction from Edward Vermilye Huntington in 1904. Huntington borrowed the symbol from Gottfried Wilhelm Leibniz in 1890 (the original date is not definitely known, but almost certainly it is written after 1685; and 1890 is the publishing time). While both Huntington in 1904 and Leibniz in 1890 used the symbol as an algebraic operation. Furthermore, Huntington in 1904 used the symbol as inclusive disjunction (logical sum) too, and in 1933 used as inclusive disjunction. , also denoting the negation of equivalence, was used by Alonzo Church in 1944. (as a prefix operator, ) was used by Józef Maria Bocheński in 1949. may mistake that it is Jan Łukasiewicz who is the first to use for exclusive disjunction (it seems that the mistake spreads widely), while neither in 1929 nor in other works did Łukasiewicz make such use. In fact, in 1949 Bocheński introduced a system of Polish notation that names all 16 binary connectives of classical logic which is a compatible extension of the notation of Łukasiewicz in 1929, and in which for exclusive disjunction appeared at the first time. Bocheński's usage of as exclusive disjunction has no relationship with the Polish "alternatywa rozłączna" of "exclusive or" and is an accident for which see the table on page 16 of the book in 1949. ^, the caret, has been used in several programming languages to denote the bitwise exclusive or operator, beginning with C and also including C++, C#, D, Java, Perl, Ruby, PHP and Python. The symmetric difference of two sets and , which may be interpreted as their elementwise exclusive or, has variously been denoted as , , or .

It is also called "not left right arrow" (\nleftrightarrow) in LaTeX based markdown Apart from the ASCII codes, the operator is encoded at and , both in block mathematical operators.