examples of contrapositive
Recall that the contrapositive of an implication^{} $p\u27f9q$ is the equivalent^{} implication $\mathrm{\neg}q\u27f9\mathrm{\neg}p$, which is read: “not $q$ implies not $p$”. The following are examples of the contrapositive and converse^{} of a logical statement:

1.
Let $p$ be the statement “it is raining” and let $q$ be “the ground is getting wet”. Then the statement “if it is raining then the ground is getting wet” is equivalent to “if the ground is not getting wet then it is not raining”. Notice that these are both true statements. Notice also that the converse would be “if the ground is getting wet then it is raining” (which is not necessarily true!).

2.
Let $f:S\to T$ be a function of sets and let $S$ be finite. The contrapositive statement of “if $f$ is surjective^{} then $T$ is finite” (a true statement) would be the implication “if $T$ is not finite then $f$ is not surjective” (also a true statement). The converse would be “if $T$ is finite then $f$ is surjective” (a false statement).
Title  examples of contrapositive 

Canonical name  ExamplesOfContrapositive 
Date of creation  20130322 16:23:05 
Last modified on  20130322 16:23:05 
Owner  alozano (2414) 
Last modified by  alozano (2414) 
Numerical id  6 
Author  alozano (2414) 
Entry type  Example 
Classification  msc 03B05 
Related topic  ConverseTheorem 