1. Entry Task Complete the Solve It activity on the top of page 106.
Which three jeans would you choose in order to spend as little as possible?
Of these pairs, which will you actually pay for?
How do you find an “average” amount?

2. Entry Task

3. Deductive Reasoning
Lesson 2-4

4. Learning Targets I will be able to:
Define deductive reasoning and give examples;
Compare and contrast deductive reasoning and inductive reasoning;
Make conclusions using the Law of Detachment and/or the Law of Syllogism;

5. What is deductive reasoning
Inductive reasoning – the process of observing data and making conjectures based on patterns you observe
Deductive reasoning – the process of making conjectures based on given statements or facts, following a logical order.

6. Consider the following statements:
If you stay up too late, then you will be tired the next day.
Mrs. Komp stayed up too late.
*assume that both statements are true*
What conclusion can you make, if any?

7. What about these statements?
If it’s Friday, then you will go to a movie.
You went to a movie.
*assume that both statements are true*
What conclusion can you make, if any?

8. Law of Detachment
If the hypothesis of a true conditional statement is true, then the conclusion must also be true.
Symbolically:

9. Examples: What can you conclude from the given information:
If there is lightning, then it is not safe to be out in the open.
Marla sees lightning from the soccer field.
It is not safe for Marla to be out in the open.
If a figure is a square, then its sides have equal length.
Figure ABCD has sides of equal length.
No conclusion

10. Now consider these statements:
If today is Wednesday, then we have activity lunch.
If we have activity lunch, then Joe goes out to eat.
What conclusion can you make from these two statements?

11. Law of Syllogism
When the conclusion of one true conditional statement is the hypothesis of another true conditional statement, you can make a conclusion from both statements.
Symbolically:

12. What about these statements?
If it is July, then you are on summer vacation.
If you work at the water park, then you are on summer vacation.
Can we conclude that it must be July?

13. What can you conclude from the given information
What can you conclude from the given information? What is your reasoning?
If a river is more than 4000 miles long, then it is longer than the Amazon.
If a river is longer than the Amazon, then it is the longest river in the world.
If a river is more than 4000 miles long, then it is the longest river in the world.
The Nile is 4132 miles long.
The Nile is the longest river in the world.

14. Your turn to practice!
Lesson Check on page 109 (1-5 all)

16. Homework
Page 110 (6-30 all)