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Xor[e1,e2,…]

is the logical XOR (exclusive OR) function. It gives True if an odd number of the ei are True, and the rest are False. It gives False if an even number of the ei are True, and the rest are False.

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Xor

Xor[e1,e2,…]

is the logical XOR (exclusive OR) function. It gives True if an odd number of the ei are True, and the rest are False. It gives False if an even number of the ei are True, and the rest are False.

Details

  • Xor[e1,e2,…] can be input in StandardForm and InputForm as e_(1) xor e_(2) xor .... The character ⊻ can be entered as xor or \[Xor].
  • Xor gives symbolic results when necessary, applying various simplification rules to them.
  • Unlike And, Nand, Or, and Nor, Xor must always test all its arguments, and so is not a control structure, and does not have attribute HoldAll.

Examples

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Basic Examples  (2)

Enter using xor:

Scope  (4)

Xor is associative and commutative:

Do symbolic simplification:

Expand in terms of And, Or, and Not:

TraditionalForm formatting:

Applications  (3)

Find the Xor of two regions in 2D:

Find the Xor of three regions in 3D:

A cellular automaton based on Xor:

Find the area of the symmetric difference of sets given by algebraic conditions:

This shows the set:

Properties & Relations  (3)

Truth table for binary Xor:

Ternary Xor:

Use BooleanConvert to expand in terms of And, Or, and Not:

Xor of conditions in Boole functions:

Neat Examples  (2)

The Xor of disks on a circle:

Generate three disks on a circle:

A truth table for a 12-variable Xor function:

Wolfram Research (1988), Xor, Wolfram Language function, https://reference.wolfram.com/language/ref/Xor.html (updated 2003).

Text

Wolfram Research (1988), Xor, Wolfram Language function, https://reference.wolfram.com/language/ref/Xor.html (updated 2003).

CMS

Wolfram Language. 1988. "Xor." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2003. https://reference.wolfram.com/language/ref/Xor.html.

APA

Wolfram Language. (1988). Xor. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Xor.html

BibTeX

@misc{reference.wolfram_2025_xor, author="Wolfram Research", title="{Xor}", year="2003", howpublished="\url{https://reference.wolfram.com/language/ref/Xor.html}", note=[Accessed: 08-August-2025]}

BibLaTeX

@online{reference.wolfram_2025_xor, organization={Wolfram Research}, title={Xor}, year={2003}, url={https://reference.wolfram.com/language/ref/Xor.html}, note=[Accessed: 08-August-2025]}