# Conditional Statements

A statement written in the
*
if-then
*
form is a conditional statement.

$p\to q$ represents the conditional statement

“if $p$ then $q$ .”

**
Example 1:
**

If two angles are adjacent , then they have a common side.

The part of the statement following
*
if
*
is called the
*
hypothesis
*
, and the part following
*
then
*
is called the conclusion.

$\text{If}\underset{\text{Hypothesis}}{\underset{\ufe38}{\text{twoanglesareadjacent,}}}\text{then}\underset{\text{Conclusion}}{\underset{\ufe38}{\text{theyhaveacommonside}\text{.}}}$

**
Example 2:
**

Identify the hypothesis and conclusion of the following statement.

A polygon is a pentagon, if it has five sides.

**
Hypothesis
**
: The polygon has five sides.

**
Conclusion
**
: It is a pentagon.

## Biconditional Statement

A biconditional statement is a combination of a conditional statement and its converse written in the
*
if and only if
*
form.

Two line segments are congruent
*
if and only if
*
they are of equal length.

It is a combination of two conditional statements, “if two line segments are congruent then they are of equal length” and “if two line segments are of equal length then they are congruent.”

A biconditional is true if and only if both the conditionals are true.

Biconditionals are represented by the symbol $\leftrightarrow $ or $\iff $ .

$p\leftrightarrow q$ means that $p\to q$ and $q\to p$ . That is, $p\leftrightarrow q=\left(p\to q\right)\wedge \left(q\to p\right)$ .

**
Example:
**

Write the two conditional statements associated with the biconditional statement below.

A rectangle is a square if and only if the adjacent sides are congruent.

The associated conditional statements are:

a) If the adjacent sides of a rectangle are congruent then it is a square.

b) If a rectangle is a square then the adjacent sides are congruent.