Converse and Contrapositive Statements/Examples
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Examples of Converse Statements and Contrapositive Statements
$x < 5$ 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
Triangles of 2 and 3 Equal Sides
Let $P$ be the statement:
which is trivially true.
$P$ can also be written:
- A sufficient condition for a triangle to have $2$ equal sides is for it to have $3$ equal sides
- A necessary condition for a triangle to have $3$ equal sides is for it to have $2$ equal sides
The converse of $P$ is:
which is false.