inverse statement
Let a statement be of the form of an implication^{}
If $p$, then $q$
i.e. (http://planetmath.org/Ie), it has a certain premise^{} $p$ and a conclusion $q$. The statement in which one has negated the conclusion and the premise,
If $\mathrm{\neg}p$, then $\mathrm{\neg}q$
is the inverse^{} (or inverse statement) of the first. Note that the following constructions yield the same statement:

•
the inverse of the original statement;

•
the contrapositive of the converse^{} of the original statement;

•
the converse of the contrapositive of the original statement.
Therefore, just as an implication and its contrapositive are logically equivalent (proven here (http://planetmath.org/SomethingRelatedToContrapositive)), the converse of the original statement and the inverse of the original statement are also logically equivalent.
The phrase “inverse theorem” is in usage; however, it is nothing akin to the phrase “converse theorem (http://planetmath.org/ConverseTheorem)”. In the phrase “inverse theorem”, the word “inverse” typically refers to a multiplicative inverse. An example of this usage is the binomial inverse theorem (http://planetmath.org/BinomialInverseTheorem).
Title  inverse statement 

Canonical name  InverseStatement 
Date of creation  20130322 17:20:00 
Last modified on  20130322 17:20:00 
Owner  Wkbj79 (1863) 
Last modified by  Wkbj79 (1863) 
Numerical id  10 
Author  Wkbj79 (1863) 
Entry type  Definition 
Classification  msc 03B05 
Synonym  inverse 
Related topic  Converse 
Related topic  SomethingRelatedToContrapositive 
Related topic  ConverseTheorem 