Difference between revisions of "Iff"

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.

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

@@ Line 3: / Line 3: @@
 In mathematical notation, "iff" is expressed as <math>\iff</math>.
-If a statement is an "iff" statement, then it is a [[conditional|biconditional]] statement.
+It is also known as a [[conditional|biconditional]] statement.
+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==
-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:
+* if <math>p</math> then <math>q</math>
+* if <math>q</math> then <math>p</math>
-* <math>p</math> implies <math>q</math> ("if <math>p</math>, then <math>q</math>")
+===Videos===
-* <math>q</math> implies <math>p</math> ("if <math>q</math>, then <math>p</math>")
+[https://www.youtube.com/embed/MckXBKafPfw Mathematical Logic]
 ==See Also==