Biconditional

Pronunciation: /ˌbaɪ.kənˈdɪ.ʃə.nl/ Explain

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.^[2] 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. McAdams, David E.. All Math Words Dictionary, biconditional. 2nd Classroom edition 20150108-4799968. pg 25. Life is a Story Problem LLC. January 8, 2015. Buy the book
2. Couturat, Louis. The Algebra of Logic. pp 6-7. Translated by Lydia Gillingham Robinson, B. www.archive.org. A.. Open Court Publishing. 1914. Last Accessed 6/19/2018. http://www.archive.org/stream/algebralogicbylc00coutrich#page/n25/mode/1up. Buy the book
3. Brennan, Joseph G.. A Handbook of Logic. 2nd edition. pg 81. www.archive.org. Harper & Row. 1961. Last Accessed 6/19/2018. http://www.archive.org/stream/handbookoflogics012674mbp#page/n90/mode/1up/search/biconditional. Buy the book
4. Cupillari, Antonella. Nuts and Bolts of Proof: An Introduction to Mathematical Proofs. 3rd edition. pg 35-44. Academic Press. August 15, 2005. Last Accessed 6/19/2018. Buy the book

More Information

• McAdams, David E.. Conjunction. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 6/22/2018. https://www.allmathwords.org/en/c/conjunction.html.

Cite this article as:

McAdams, David E. Biconditional. 4/12/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/b/biconditional.html.

Revision History

4/12/2019: Changed equations and expressions to new format. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
6/22/2018: Removed broken links, updated license, implemented new markup. (McAdams, David E.)
1/8/2010: Added "References". (McAdams, David E.)
6/28/2008: Added hot link for equivalence relation; added dictionary.com to More Information (McAdams, David E.)
2/5/2008: Changed wording to clarify. Removed ↔ to image biconditional.gif (McAdams, David E.)
8/20/2007: Added revision history. Removed spurious ';' (McAdams, David E.)
7/15/2007: Initial version. (McAdams, David E.)