Xnor

Xnor[e1,e2,…]

is the logical XNOR (not XOR) function. It gives True if an even number of the e_(i) are True, and the rest are False. It gives False if an odd number of the e_(i) are True, and the rest are False.

Details

  • Xnor[e1,e2,…] can be input in StandardForm and InputForm as eie2…. The character can be entered as xnor or \[Xnor].
  • Xnor gives symbolic results, applying various simplification rules automatically.
  • Unlike And, Nand, Or, and Nor, Xnor must always test all its arguments, so is not a control structure, and does not have attribute HoldAll.

Examples

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Basic Examples  (3)

Xnor in disjunctive normal form:

Enter using xnor:

Scope  (1)

Automatic simplifications:

Elimination of constants:

Xnor is commutative and sorts its arguments:

Properties & Relations  (5)

Truth table for binary Xnor:

Ternary Xnor:

Xnor in variables has a disjunctive normal form of length :

Xnor is equivalent to the negation of Xor:

For two variables Xnor is the same as Equivalent:

But they differ for more than two variables:

Xnor is a special case of BooleanCountingFunction:

Neat Examples  (1)

The 2D truth table for Xnor of 12 variables:

Wolfram Research (2008), Xnor, Wolfram Language function, https://reference.wolfram.com/language/ref/Xnor.html.

Text

Wolfram Research (2008), Xnor, Wolfram Language function, https://reference.wolfram.com/language/ref/Xnor.html.

CMS

Wolfram Language. 2008. "Xnor." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/Xnor.html.

APA

Wolfram Language. (2008). Xnor. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Xnor.html

BibTeX

@misc{reference.wolfram_2025_xnor, author="Wolfram Research", title="{Xnor}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/Xnor.html}", note=[Accessed: 21-February-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_xnor, organization={Wolfram Research}, title={Xnor}, year={2008}, url={https://reference.wolfram.com/language/ref/Xnor.html}, note=[Accessed: 21-February-2025 ]}