Exclusive Disjunction (XOR) ○◂

|↑| Disjunction (OR) ○◂ | Exclusive Disjunction (XOR) ○◂ ⦍∂₁ₐ’⦎_
⮞ 🟣 𓂃𓂃𓂃
⮞ ➔ Exclusive Non-Disjunction (XNOR) ○◂ 🗘
⮞ ⛛ 𓂃𓂃𓂃

• XOR Gate ○꠹ …

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Exclusive Disjunction (XOR) ○◂｜Definition｜1st｜20251119205401-00-⌔

Exclusive or - Wikipedia

Exclusive or

📊 ➺ 🖼️ ➺ 🖼️ ➺ 🖼️ ➺

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.¹

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 $J$²${}^{:16}$ and by the infix operators XOR (/ˌɛks ˈɔːr/or/ˈksɔːr/), EOR, EXOR, $\dot{\vee }$, $\overline{\vee }$, $\underline{\vee }$, ⩛, $\oplus$, $\nleftrightarrow$, $\not\equiv$, and

Printed 2026-06-28.

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Footnotes

1. Germundsson, Roger; Weisstein, Eric. “XOR”. MathWorld. Wolfram Research. Retrieved 17 June 2015. ↩

2. Bocheński, J. M. (1949). Précis de logique mathématique (PDF) (in French). The Netherlands: F. G. Kroonder, Bussum, Pays-Bas. Translated as Bocheński, J. M. (1959). A Precis of Mathematical Logic. Translated by Bird, O. Dordrecht, Holland: D. Reidel Publishing Company. doi:10.1007/978-94-017-0592-9. ISBN 978-90-481-8329-6. ↩

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