1. Section 2.2 Analyze Conditional Statements

2. What is an if-then statement?
If-then statements can be used to clarify statements that may seem confusing.
These statements are logic statements.
Logic statements are important in many different types of professions.

3. Examples: If the sun shines, then the grass will grow.
If I live in NJ, then I live on the east coast.
If the month is January, then next month is February.

4. These if-then statements are called conditional statements or conditionals.
Conditional Statement: A logical statement that has two parts.
In general, these conditionals are written:
If p, then q or p q.
Where p is the hypothesis and
q is the conclusion.

5. Let’s take a look back at our examples:
If the sun shines, then the grass will grow.
If I live in NJ, then I live on the east coast.
If the month is January, then next month is February.

6. Write the conditional statement in if-then form: The car will run if there is gas in the tank. I will wake up on time if my alarm goes off.
If there is gas in the tank, then the car will run.
If my alarm goes off, then I will wake up on time.

7. Converse: Exchange the hypothesis and conclusion of the conditional.
The converse of p q is q p.
Conditional: If I live in NJ, then I live on the east coast.
Converse: If I live on the east coast, then I live in NJ.
True!
False!

8. The denial of a statement is called a negation.
~p represents “not p”
3.) This is geometry.
This is not geometry.
4.) Today is not Thursday.
Today is Thursday.
1.) An angle is obtuse.
An angle is not obtuse.
2.) A puppy is a dog.
A puppy is not a dog.

9. The inverse of a conditional can be formed by negating both the hypothesis and conclusion.
~p ~q
If-then Statement: If you are from Mexico, then you speak Spanish.
Inverse: If you are not from Mexico, then you do not speak Spanish.

10. Contrapositive: ~q ~p
If-then statement: If you lift weights, then you will be strong.
Contrapositive: If you are not strong, then you do not lift weights.

11. Quick Review If-then statement: If p, then q. Converse: If q, then p.
Inverse: If ~p, then ~q.
Contrapositive: If ~q, then ~p.

12. Let’s put it all together!
If-then statement: If you live in Red Bank, NJ, then you live in Monmouth County.
Converse: If you live in Monmouth County, then you live in Red Bank, NJ.
Inverse: If you do not live in Red Bank, NJ, then you do not live in Monmouth County.
Contrapositive: If you do not live in Monmouth County, then you do not live in Red Bank, NJ.