 # Exclusive or

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Exclusive or or exclusive disjunction or exclusive alternation, also known as non-equivalence which is the negation of equivalence, is a logical operation that is true if and only if its arguments differ (one is true, the other is false).

Quick facts: XOR, Truth table, Logic gate, Normal forms, D...
Exclusive or
XOR Truth table$(0110)$ Logic gate Normal forms
Disjunctive${\overline {x}}\cdot y+x\cdot {\overline {y}}$ Conjunctive$({\overline {x}}+{\overline {y}})\cdot (x+y)$ Zhegalkin polynomial$x\oplus y$ Post's lattices
0-preservingyes
1-preservingno
Monotoneno
Affineyes
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It is symbolized by the prefix operator $J$ :16 and by the infix operators XOR (/ˌɛks ˈɔːr/, /ˌɛks ˈɔː/, /ˈksɔːr/ or /ˈksɔː/), EOR, EXOR, ${\dot {\vee }}$ , ${\overline {\vee }}$ , ${\underline {\vee }}$ , , $\oplus$ , $\nleftrightarrow$ and $\not \equiv$ .