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Xor—Wolfram Documentation

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

Examples

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Basic Examples  (2)

Enter using xor:

Scope  (4)

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)

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:

History

Introduced in 1988 (1.0) | Updated in 2003 (5.0)

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: 22-February-2026]}

BibLaTeX

@online{reference.wolfram_2025_xor, organization={Wolfram Research}, title={Xor}, year={2003}, url={https://reference.wolfram.com/language/ref/Xor.html}, note=[Accessed: 22-February-2026]}