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aliases: [exclusive or, exclusive OR, XOR, xor]
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#logic
> [!tldr] Definition
> The **exclusive or**, abbreviated **XOR**, is a logical [[Connectives|connective]] joining two [[Propositions|propositions]], which results in a new proposition that is true only when one of the propositions, *but not both*, is true. The notation for a conjunction is the symbol $\oplus$, and we pronounced $A \oplus B$ as "$A$ XOR $B
quot;.
Notes:
- The [[Truth tables|truth table]] for $A \oplus B$ is:
| $A$ | $B$ | $A \oplus B$ |
| ----- | ----- | ------------ |
| True | True | False |
| True | False | True |
| False | True | True |
| False | False | False |
Again, $A \oplus B$ is true only *exactly one* of $A$ or $B$ is true.
- The [[Disjunction|disjunction]] $A \vee B$ is an "inclusive or" because $A \vee B$ is true if either $A$ or $B$, *or both*, is true.