Exclusive or or exclusive disjunction is a logical operation that is true if and only if its arguments differ (one is true, the other is false).
It is symbolized by the prefix operator J and by the infix operators XOR (/ˌɛks ˈɔːr/, /ˌɛks ˈɔː/, /ˈksɔːr/ or /ˈksɔː/), EOR, EXOR, ⊻, ⩒, ⩛, ⊕, and ≢. The negation of XOR is the logical biconditional, which yields true iff the two inputs are the same.
It gains the name "exclusive or" because the meaning of "or" is ambiguous when both operands are true; the exclusive or operator excludes that case. This is sometimes thought of as "one or the other but not both". This could be written as "A or B, but not A and B".
Since it is associative, it may be considered to be an n-ary operator which is true if and only if an odd number of arguments are true. That is, a XOR b XOR ... may be treated as XOR(a,b,...).
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The truth table of A XOR B shows that it outputs true whenever the inputs differ:
| A | B | A ⊕ B |
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| F | F | F |
| F | T | T |
| T | F | T |
| T | T | F |
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