Difference between revisions of "Iff"

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In mathematical notation, "iff" is expressed as <math>\iff</math>.
 
In mathematical notation, "iff" is expressed as <math>\iff</math>.
  
If a statement is an "iff" statement, then it is a [[conditional|biconditional]] statement.
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It is also known as a [[conditional|biconditional]] statement.
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An iff statement <math>p\iff q</math> means <math>p\implies q</math> <b>and</b> <math>q\implies p</math> at the same time.
  
 
==Example==
 
==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:  
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In order to prove a statement of the form "<math>p</math> iff <math>q</math>," it is necessary to prove two distinct implications:  
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* if <math>p</math> then <math>q</math>
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* if <math>q</math> then <math>p</math>
  
* <math>p</math> implies <math>q</math> ("if <math>p</math>, then <math>q</math>")
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===Videos===
* <math>q</math> implies <math>p</math> ("if <math>q</math>, then <math>p</math>")
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[https://www.youtube.com/embed/MckXBKafPfw Mathematical Logic]
  
 
==See Also==
 
==See Also==

Revision as of 16:45, 31 July 2020

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

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

It is also known as a biconditional statement.

An iff statement $p\iff q$ means $p\implies q$ and $q\implies p$ at the same time.

Example

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

  • if $p$ then $q$
  • if $q$ then $p$

Videos

Mathematical Logic

See Also

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