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.


  1. biconditional. WordNet. Princeton University. (Accessed: 2011-01-08).
  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).
  3. Brennan, Joseph G.. A Handbook of Logic, 2nd edition, pg 81. Harper & Row, 1961. (Accessed: 2010-01-08).
  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. All Math Words Encyclopedia. Life is a Story Problem LLC. 2009-03-12.

Printed Resources

Cite this article as:

Biconditional. 2010-01-08. All Math Words Encyclopedia. Life is a Story Problem LLC.


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Revision History

2010-01-08: Added "References" (McAdams, David.)
2008-06-28: Added hot link for equivalence relation; added 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.)

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