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
- 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=.
- 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.
- 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.
- 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 LLC. 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 LLC. http://www.allmathwords.org/en/b/biconditional.html.
Translations
Image Credits
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.)