Difference between revisions of "Iff"

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'''Iff''' is an abbreviation for the phrase "if and only if."
 
'''Iff''' is an abbreviation for the phrase "if and only if."
  
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In mathematical notation, "iff" is expressed as <math>\iff</math>.
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If a statement is an "iff" statement, then it is a [[conditional|biconditional]] statement.
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==Example==
 
In order to prove a statement of the form, "<math>p</math> iff <math>q</math>," it is necessary to prove two distinct implications:  
 
In order to prove a statement of the form, "<math>p</math> iff <math>q</math>," it is necessary to prove two distinct implications:  
  
 
* <math>p</math> implies <math>q</math> ("if <math>p</math>, then <math>q</math>")
 
* <math>p</math> implies <math>q</math> ("if <math>p</math>, then <math>q</math>")
 
* <math>q</math> implies <math>p</math> ("if <math>q</math>, then <math>p</math>")
 
* <math>q</math> implies <math>p</math> ("if <math>q</math>, then <math>p</math>")
 
If a statement is an "iff" statement, then it is a [[conditional|biconditional]] statement.
 
  
 
==See Also==
 
==See Also==

Revision as of 12:35, 26 January 2013

Iff is an abbreviation for the phrase "if and only if."

In mathematical notation, "iff" is expressed as $\iff$.

If a statement is an "iff" statement, then it is a biconditional statement.

Example

In order to prove a statement of the form, "$p$ iff $q$," it is necessary to prove two distinct implications:

  • $p$ implies $q$ ("if $p$, then $q$")
  • $q$ implies $p$ ("if $q$, then $p$")

See Also

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