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.