1. Chapter 2
Reasoning and Proof

2. 2-1 Conditional Statements

3. “If you are in this room, then you are not outside”
Mrs. Moore
Geometry class
MacArthur High School
1975

4. A conditional statement is an if-then statement.
If you are 16, then you can get a driver’s license.
If you attend Lafayette, then you are a Lancer.

5. Each conditional statement has two parts:
The hypothesis follows the “if”.
The conclusion follows the “then”.
If you attend Lafayette, then you are a Lancer.
Conclusion
Hypothesis

6. If you attend Lafayette, then you are a Lancer.
Conclusion
Hypothesis
Note: the hypothesis does not include the word “if”; the conclusion does not include the word “then”.

7. Identify the hypothesis and conclusion:
If I live in Missouri, then I live in the United States.
If I eat carrots, then I will have good eyesight.
If it is raining, then the ground will get wet.

8. Write the statement as a conditional.
Cats have tails.
Monday is a weekday.
Geometry is awesome!

9. Conditionals have a truth value. A conditional can be true or false
Conditionals have a truth value. A conditional can be true or false. If you find a counterexample, the truth value is false.
If it is the weekend, then it is Saturday.

10. Indicate whether the conditional is true or false
Indicate whether the conditional is true or false. If false, find a counterexample:
If you live in the United States, then you live in Missouri.
If it is Oct. 31, then it is Halloween.

11. The converse of a conditional switches the hypothesis and conclusion
The converse of a conditional switches the hypothesis and conclusion. A converse also has a truth value:
If you live in Florida, then you live in the United States.
If you live in the United States, then you live in Florida.
Conditional
Converse

12. Find the converse. Indicate the truth value of the conditional and its converse.
If it is Monday, then it is a weekday.
If the month is September, then the month has 30 day.
If you are in room 247 (this room), then you are in this building.
If it is Feb. 14, then it is Valentine’s Day.

13. Homework: p , , ,