Purpose

1. Over the years you have made conjectures, using inductive reasoning, based on patterns you have observed. When you make a conjecture, the process of discovery may not always help explain why the conjecture works. You need another kind of reasoning to help answer this question. Purpose

2. Deductive Reasoningis the process of showing that certain statements follow logically from agreed-upon assumptions and proven facts. • When you use deductive reasoning, you try to reason in an orderly way to convince others that your conclusion is valid. • Examples: Lawyers use deductive arguments to prove their case to a jury. Every time you show your work in a math problem you are using deductive reasoning…. Let’s see an example… What do we need then?

3. 3(2x+1) + 2(2x+1) + 7 = 42 – 5x 5(2x+1) + 7 = 42 – 5x 5(2x+1) = 35 – 5x 10x + 5 = 35 – 5x 10x = 30 – 5x 15x = 30 x = 2 Example: Solve for x. This is the work you are used to showing when solving algebraic equations.

4. Example: Solve for x, give reasons for each step. Here we have given specific reasons for each step and have formed a logical argument that x=2. *This is deductive reasoning.*

5. If Manuel has a healthy diet, then he will have a healthy body. If Manuel has a healthy body, then he will feel good. Syllogism: If Manuel has a healthy diet, then he will feel good. Would you use the Law of Detachment or law of Syllogism in the following example?How would you rewrite the final conditional statement?

6. If the season is Fall, then the leaves will change colors. If the leaves change colors, then they will fall from the trees. Would you use the Law of Detachment or law of Syllogism in the following example?How would you rewrite the final conditional statement? • Syllogism: If the season is Fall, then the leaves will fall from the trees!

7. Would you use the Law of Detachment or law of Syllogism in the following example?How would you rewrite the final conditional statement? If you are at least 16 years old, you can get a drivers license. Ricky is 16 years old. Detachment: Ricky can get a drivers license.

8. If 2x > 10, then 2x > 7. If x > 5, then 2x > 10. Would you use the Law of Detachment or law of Syllogism in the following example?How would you rewrite the final conditional statement? • Syllogism: If x > 5, then 2x > 7.

9. Would you use the Law of Detachment or law of Syllogism in the following example?How would you rewrite the final conditional statement? If you study hard, you will pass all of your classes. If you pass all of your classes, you will graduate. Syllogism: If you study hard, then you will graduate.

10. Would you use the Law of Detachment or law of Syllogism in the following example?How would you rewrite the final conditional statement? If x2 > 9, then x2 > 8. If x > 4, then x2 > 9. Syllogism: If x > 4 , then x2 > 8.

11. Would you use the Law of Detachment or law of Syllogism in the following example?How would you rewrite the final conditional statement? If you like pizza, you love Chicago style deep dish. Emily loves Chicago style deep dish. Detachment: Emily loves pizza.

12. Would you use the Law of Detachment or law of Syllogism in the following example?How would you rewrite the final conditional statement? If Ron eats lunch today, then he will eat a sandwich. If Ron eats a sandwich, then he will drink a glass of milk. Syllogism: If Ron eats lunch today, then he will drink a glass of milk.

13. Would you use the Law of Detachment or law of Syllogism in the following example?How would you rewrite the final conditional statement? If you want an “A” in Geometry, you will have to study hard. Sal is studying hard. Detachment: Sal will get an “A” in Geometry.

14. Would you use the Law of Detachment or law of Syllogism in the following example?How would you rewrite the final conditional statement? If you do your homework, then you can watch TV. If you watch TV, then you can watch your favorite show Syllogism: If you do your homework, then you can watch your favorite TV show.

15. Would you use the Law of Detachment or law of Syllogism in the following example?How would you rewrite the final conditional statement? If Kendra pops a bag of popcorn, then she will eat the popcorn. If Kendra eats the popcorn, then she will need something to drink. Syllogism: If Kendra pops a bag of popcorn, then she will need something to drink.

16. If you give Kfed money, then he makes an awesome album. • Hypothesis- • Conclusion-

17. The ______ of a conditional statement is formed by exchanging the hypothesis and the conclusion. • Conditional- If it is sunny outside, then it is hot. • Converse- If it is hot, then it is sunny outside.

18. What are the key words included in a biconditional statement?

19. What is the inverse of the following statement. Example: Cond. Stmt: If is sunny outside, then it is hot. Inverse: If it is NOT sunny outside, then it is NOT hot.

20. What is the contrapositive for the following statement? If it is sunny outside, then it is hot. Example: Cond. Stmt: If it is sunny outside, then it is hot. Converse: If it is hot, then it is sunny outside. Contrapositive:If it is NOT hot, then it is NOT sunny.