Symmetric Difference

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1	handwiki	Sirius Huang	--	2049	2022-10-17 01:43:18

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HandWiki. Symmetric Difference. Encyclopedia. Available online: https://encyclopedia.pub/entry/29476 (accessed on 29 September 2026).

HandWiki. Symmetric Difference. Encyclopedia. Available at: https://encyclopedia.pub/entry/29476. Accessed September 29, 2026.

HandWiki. "Symmetric Difference" Encyclopedia, https://encyclopedia.pub/entry/29476 (accessed September 29, 2026).

HandWiki. (2022, October 17). Symmetric Difference. In Encyclopedia. https://encyclopedia.pub/entry/29476

HandWiki. "Symmetric Difference." Encyclopedia. Web. 17 October, 2022.

Symmetric Difference

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The content is sourced from: https://handwiki.org/wiki/Symmetric_difference

In mathematics, the symmetric difference, also known as the disjunctive union, of two sets is the set of elements which are in either of the sets and not in their intersection. The symmetric difference of the sets A and B is commonly denoted by or or For example, the symmetric difference of the sets [math]\displaystyle{ \{1,2,3\} }[/math] and [math]\displaystyle{ \{3,4\} }[/math] is [math]\displaystyle{ \{1,2,4\} }[/math]. The power set of any set becomes an abelian group under the operation of symmetric difference, with the empty set as the neutral element of the group and every element in this group being its own inverse. The power set of any set becomes a Boolean ring with symmetric difference as the addition of the ring and intersection as the multiplication of the ring.

symmetric difference abelian group power set

References

Givant, Steven; Halmos, Paul (2009). Introduction to Boolean Algebras. Springer Science & Business Media. p. 6. ISBN 978-0-387-40293-2.
Humberstone, Lloyd (2011). The Connectives. MIT Press. p. 782. ISBN 978-0-262-01654-4. https://archive.org/details/connectives00humb.
Rotman, Joseph J. (2010). Advanced Modern Algebra. American Mathematical Soc.. p. 19. ISBN 978-0-8218-4741-1.
Rudin, Walter (January 1, 1976). Principles of Mathematical Analysis (3rd ed.). McGraw-Hill Education. p. 306. ISBN 978-0070542358. https://archive.org/details/principlesofmath00rudi.
Claude Flament (1963) Applications of Graph Theory to Group Structure, page 16, Prentice-Hall MR0157785 https://mathscinet.ams.org/mathscinet-getitem?mr=0157785

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