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Exclusive disjunction facts for kids

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Venn0110.svg
Venn diagram of \scriptstyle A \oplus B

OR but not AND is XOR

Venn 0110 1001.svg
Venn diagram of \scriptstyle A \oplus B \oplus C

Venn 0110 0110.svg ~\oplus~ Venn 0000 1111.svg ~\Leftrightarrow~ Venn 0110 1001.svg

Exclusive disjunction (also called exclusive or, XOR) is a logic operation on two values. It is often represented by the symbol \veebar (or \oplus). It will be true, if exactly one of the two values is true. Otherwise, it will be false. This also means that the result of 'XOR' will be true precisely both the values are different. Same values will result in a false.

The best way to remember a XOR operation is: "One or the other, but not both".

Because of that, this is different from inclusive disjunction.

Truth table

The truth table of p\, \mathrm{XOR}\, q (also written as p \oplus q, p \veebar q, or p \neq q) is as follows:

p q
F F F
F T T
T F T
T T F

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