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.^{[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
- 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 8/6/2018. http://www.archive.org/stream/algebralogicbylc00coutrich#page/n25/mode/1up. Buy the book
- Brennan, Joseph G.. A Handbook of Logic. 2nd edition. pg 81. www.archive.org. Harper & Row. 1961. Last Accessed 8/6/2018. http://www.archive.org/stream/handbookoflogics012674mbp#page/n90/mode/1up/search/biconditional. Buy the book
- Cupillari, Antonella. Nuts and Bolts of Proof: An Introduction to Mathematical Proofs. 3rd edition. pg 35-44. Academic Press. August 15, 2005. Last Accessed 8/6/2018. Buy the book
More Information
- McAdams, David E.. Conjunction. allmathwords.org. All Math Words Encyclopedia. Life is a Story Problem LLC. 6/22/2018. http://www.allmathwords.org/en/c/conjunction.html.
Cite this article as:
McAdams, David E. Biconditional. 6/19/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/b/biconditional.html.
Revision History
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.)