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."
  
In order to prove a statement of the form, "A iff B," it is necessary to prove two distinct implications: that A implies B ("if A then B") and that B implies A ("if B then A"). 
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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:  
  
If a statement is an "iff" statement, then it is a [[biconditional]] statement.
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* <math>p</math> implies <math>q</math> ("if <math>p</math>, then <math>q</math>")
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* <math>q</math> implies <math>p</math> ("if <math>q</math>, then <math>p</math>")
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If a statement is an "iff" statement, then it is a [[conditional|biconditional]] statement.
  
 
==See Also==
 
==See Also==
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* [[Logic]]
  
[[logic]]
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{{stub}}
  
 
[[Category:Definition]]
 
[[Category:Definition]]
 
{{stub}}
 

Revision as of 14:40, 19 April 2008

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

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 $p$")

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

See Also

This article is a stub. Help us out by expanding it.

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