Biconditional

Pronunciation: /ˌbaɪ kənˈdɪ ʃə nl/ ?

The term biconditional is an equivalence relationship stating that, given statements A and B, the truth value of A is identical to the truth value of B.^[1] There are four ways this relationship is commonly written:

• A if and only if B;
• A iff B (iff is an abbreviation of 'if and only if');
• A ⇔ B; and
• A ≡ B.

For the purposes of middle school and high school math, these four equivalence relationships can be considered to be the same.

References

1. biconditional. http://wordnet.princeton.edu/. WordNet. Princeton University. (Accessed: 2011-01-08). http://wordnetweb.princeton.edu/perl/webwn?s=biconditional&sub=Search+WordNet&o2=&o0=1&o7=&o5=&o1=1&o6=&o4=&o3=&h=.
2. Louis Couturat. The Algebra of Logic, pp 6-7. English translation by Lydia Gillingham Robinson, B. A.. Open Court Publishing, 1914. (Accessed: 2009-12-19). http://www.archive.org/stream/algebralogicbylc00coutrich#page/n25/mode/1up.
3. Brennan, Joseph G.. A Handbook of Logic, 2nd edition, pg 81. Harper & Row, 1961. (Accessed: 2010-01-08). http://www.archive.org/stream/handbookoflogics012674mbp#page/n90/mode/1up/search/biconditional.
4. Cupillari, Antonella. Nuts and Bolts of Proof: An Introduction to Mathematical Proofs, 3rd edition, pg 35-44. Academic Press. (Accessed: 2010-01-11).

More Information

• McAdams, David. Conjunction. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem.org. 2009-03-12. http://www.allmathwords.org/article.aspx?lang=en&id=Conjunction.

Printed Resources

Cite this article as:

Biconditional. 2010-01-08. All Math Words Encyclopedia. Life is a Story Problem.org. http://www.allmathwords.org/en/b/biconditional.html.

Translations

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Image Credits

• All images and manipulatives are by David McAdams unless otherwise stated. All images by David McAdams are Copyright © Life is a Story Problem.org and are licensed under the Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Revision History

2010-01-08: Added "References" (McAdams, David.)
2008-06-28: Added hot link for equivalence relation; added dictionary.com to More Information (McAdams, David.)
2008-02-05: Changed wording to clarify. Removed ↔ to image biconditional.gif (McAdams, David.)
2007-08-20: Added revision history. Removed spurious ';' (McAdams, David.)
2007-07-15: Initial version (McAdams, David.)