Converse and Contrapositive Statements/Examples/x less than 5 and x less than or equal to 5

Examples of Converse Statements and Contrapositive Statements

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.

Sources

• 1978: Thomas A. Whitelaw: An Introduction to Abstract Algebra ... (previous) ... (next): Chapter $1$: Sets and Logic: Exercise $2$