# Xnor

Xnor[e1,e2,]

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

open allclose all

## 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_2023_xnor, author="Wolfram Research", title="{Xnor}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/Xnor.html}", note=[Accessed: 04-March-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2023_xnor, organization={Wolfram Research}, title={Xnor}, year={2008}, url={https://reference.wolfram.com/language/ref/Xnor.html}, note=[Accessed: 04-March-2024 ]}