# Conditionals

### Conditionals

#### Lessons

Notes:

A conditional statement is a statement written in the form "if, then".
The phrase after the word "if" is called a hypothesis.
The phrase after the word "then" is called the conclusion.
In symbolic form the conditional statement is written as:

$p \to q$

Where $p$ is the hypothesis, $q$ is the conclusion, and $\to$ implies it is an "if, then" statement.
• Introduction
Conditionals Overview:
a)
What are Conditionals?

b)
Truth Table for Conditionals

• 1.
Hypothesis and Conclusions

Identify the Hypothesis and Conclusion:

a)
If Patsy has a messy hair today, then she will not show up to work.

b)
If two lines are parallel, then they will not intersect.

c)
If a polygon has 3 sides, then it is a triangle.

d)
If the dog is barking, then someone is nearby.

• 2.
Write each statement in "if, then" form:
a)
The sum of the angles of a 3-sided polygon is 180&#deg;.

b)
In a clear night, we can see the moon.

c)
Getting a bachelor's degree will get you a job.

• 3.
Truth value of Conditionals

Determine the truth value of the following conditional statements. If it is false, then find a counterexample:

a)
If $a \leq 3$, then $a > 3$

b)
If two lines intersect, then it must create a right angle

c)
If $a=1$, $b=2$, $c=3$, then $a+b+c>5$

d)
If a polygon has 3 sides, then it is a triangle.

• 4.
Determine the truth value of the statement below for each set of conditions:

If I sleep for more than 8 hours, then you will be not tired

a)
I sleep for 9 hours and I am not tired

b)
I sleep for 9 hours and I am tired

c)
I sleep for 6 hours and I am tired

d)
I sleep for 5 hours and I am not tired

e)
I sleep for 8 hours and I am tired