# 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

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

McAdams, David E. Biconditional. 4/12/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. http://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.)