1. Entry Task

2. Using Deductive Reasoning 2.4 Learning Target: Given a true statement I can use deductive reasoning to make valid conclusions

3. Deductive Reasoning –(aka logical reasoning) a process of reasoning logically from given facts to a conclusion

4. A mechanic uses deductive reasoning to determine what is wrong with your car. 2-3 Using Deductive Reasoning to Verify Conjectures

5. A doctor will use deductive reasoning to diagnose a patient. 2-3 Using Deductive Reasoning to Verify Conjecture

6. A lawyer uses deductive reasoning to build a case. 2-3 Using Deductive Reasoning to Verify Conjectures

7. A construction foreman uses deductive reasoning to determine what materials are needed at a work site. 2-3 Using Deductive Reasoning to Verify Conjectures

8. And of course a detective uses deductive reasoning to solve crimes. 2-3 Using Deductive Reasoning to Verify Conjectures

9. Deductive Reasoning The process of reasoning using logic to draw Conclusion from given facts, definitions, and properties AKA logical reasoning.

10. Deductive vs. Inductive Reasoning The difference: inductive reasoning uses patterns to arrive at a conclusion (conjecture) deductive reasoning uses facts, rules, definitions or properties to arrive at a conclusion. Day 1

11. Examples of Inductive Reasoning Some examples 1)Every quiz has been easy. Therefore, the test will be easy. 2)The teacher used PowerPoint in the last few classes. Therefore, the teacher will use PowerPoint tomorrow. 3)Every fall there have been hurricanes in the tropics. Therefore, there will be hurricanes in the tropics this coming fall.

12. Deductive Reasoning The catalog states that all entering freshmen must take a mathematics placement test. Conclusion: You will have to take a mathematics placement test. You are an entering freshman. An Example: Day 1

13. Deductive Reasoning There are two laws used in logical reasoning: LAW OF DETACHMENT LAW OF SYLLOGISM

14. Law of Detachment

15. Deductive Reasoning LAW OF DETACHMENT This law states that if a conditional statement is true, and Its hypothesis is true, then its conclusion is true. Example: If it is raining outside, then I will use my umbrella. It is raining outside What can you conclude? I will use my umbrella. If p q is a true statement and p is true, Then q is true. Day 1

16. Law of Syllogism

17. Deductive Reasoning LAW OF SYLLOGISM If Tony goes to the movies, then he will eat popcorn. If Tony eats popcorn, he will get indigestion. Conclusion: If Tony goes to the movies, then he will get Indigestion. pq q r pr

19. Let’s Check If possible make a conclusion….. 1) If it is Tuesday, then you will go bowling. You go bowling. 2) If it is Saturday then you walk to work. If you walk to work then you wear your sneakers. No, you can’t make a conclusion. The last statement relates to the conclusion and not the hypothesis. Yes, if it is Saturday, then you wear sneakers.

21. Homework Homework: P. 110 #7-29 odds not 25 Challenge – 32