Definition:Contrapositive Statement

From ProofWiki
Jump to: navigation, search

Definition

The contrapositive of the conditional:

$p \implies q$

is the statement:

$\neg q \implies \neg p$


Examples

$x < 5$ and $x \le 5$

Let:

$P$ be the statement $x < 5 \implies x \le 5$
$Q$ be the statement $x \le 5 \implies x < 5$
$R$ be the statement $x > 5 \implies x \ge 5$
$S$ be the statement $x \ge 5 \implies x > 5$

for $x \in \R$.


Then:

$P$ and $Q$ are converse statements
$R$ and $S$ are converse statements
$P$ and $R$ are contrapositive statements
$Q$ and $S$ are contrapositive statements
$P$ and $R$ are true
$Q$ and $S$ are false.


Also see


Sources