1. 2.2 Inductive and Deductive Reasoning

2. Deductive reasoning is the process of reasoning logically from given statements to a conclusion.

3. 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.

4. Examples of Inductive Reasoning 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.

5. Examples of 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.

6. Inductive or Deductive Reasoning? 60 ◦ x Triangle sum property - the sum of the angles of any triangle is always 180 degrees. Therefore, angle x = 30° What is the measure of angle x? Deductive Reasoning – conclusion is based on a property

7. Inductive or Deductive Reasoning? Geometry example… What is the next shape in the sequence? Inductive Reasoning- conclusion based off of pattern

8. Deductive Reasoning Law of Detachment If a conditional is true and its hypothesis is true, then its conclusion is true. If P Q is a true statement and p is true, then q is true.

9. 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.

10. If it is snowing, then the temperature is less than or equal to 32˚F. The temperature is 20˚F. It is not possible to conclude that it is snowing.

11. You try! Use the law of detachment to draw a conclusion. If a baseball player is a pitcher, then that player should not pitch a complete game two days in a row. Brent is a pitcher. On Monday, he pitches a complete game. What can you conclude? Brent should not pitch a complete game on Tuesday.

12. You try!! Use the Law of Detachment to draw a conclusion, if possible. If two lines are parallel, then they do not intersect. Line a is parallel to line b. Line a will not intersect line b

13. You try! If three points lie on the same line, then they are collinear. Points A, B, and C lie on line l. Points A, B and C are collinear

14. You try! If a road is icy, then driving conditions are hazardous. Driving conditions are hazardous. It is not possible to conclude that it is icy.

15. Deductive Reasoning LAW OF SYLLOGISM If p q and q r are true statements, then p r is a true statement

16. 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

17. Deductive Reasoning LAW OF SYLLOGISM Example: If it rains outside, the walkway will get wet. If the walkway is wet, the walkway will be slippery. What can we conclude from the Law of Syllogism? Conclusion: If it is raining, the walkway will be slippery.

18. You Try! Can you use Law of syllogism? If a team wins 10 games, then they play in the finals. If a team plays in the finals, then they travel to Boston. The Ravens won 10 games. Conclusion:The Ravens will travel to Boston.