If (-3,y) is a solution to the equation -2x+7y=-8, what is the value for y ?

1. 3.1 warm-up If (-3,y) is a solution to the equation -2x+7y=-8, what is the value for y ? a. -61/2 b. -2 c. -2/7 d. 2 4

2. 3.1 warm-up If (-3,y) is a solution to the equation -2x+7y=-8, what is the value for x ? a. -61/2 b. -2 c. 2/7 d. 2 4

3. 2.3 Deductive Reasoning You will use logical reasoning to prove statements are true. You will also use deductive reasoning to prove a statement. By Pardekooper & Meadows

4. Deductive Reasoning takes place when you use the laws of reasoning to reach conclusions.

5. Law of Detachment If p → q and p is true, then q is true. p implies q If you have a true conditional and the hypothesis is true, then the conclusion is also true.

6. Example: If two numbers are odd, then their sum is even, and 3 and 5 are odd. What conclusion can be drawn, if any? The sum of 3 and 5 is even.

7. Example: If it is raining outside, then Mr. Nava has his umbrella, and Mr. Nava has his umbrella. It must be raining. What conclusion can be drawn, if any?

8. Law of Syllogism If p → q and q→ r, then p → r. If p is the hypothesis and q is the conclusion for one conditional and q is the hypothesis with r as the conclusion for a second conditional, then you can draw a conclusion that is a conditional with p as the hypothesis and r as the conclusion.

9. Example: If you pass this class, then you study. If you study, then you have red hair. Assuming the previous two conditionals are true statements, what conclusion can you draw, if any? If you pass this class, then you have red hair.

10. Example: If a pet is a dog, then it has 4 legs. If a pet is a dog, then it barks.  Assuming the previous two conditionals are true statements, what conclusion can you draw, if any? none

11. Example: Draw a conclusion, if possible, and state the law that applies. If someone is tall, then they have big feet. Law of syllogism If someone is tall, then their family is tall. If someone’s family is tall, then they all have big feet.

12. Example: Draw a conclusion, if possible, and state the law that applies. You must be wearing a coat. If you are wearing a coat, then it is cold outside. Law of detachment The temperature is 57 degrees.

13. Example: Draw a conclusion, if possible, and state the law that applies. none If you read, then you love to dance. Law of detachment You read one novel every week.

14. Assignment

15. Geometry 2.3 Deductive Reasoning Use the Law of Detachment to draw a conclusion. 1. If the football team wins on Friday night, then practice is canceled for Monday. The football team won by 7 points on Friday night. Use the Law of Syllogism to draw a conclusion 2. If you like the movie, then you saw a good movie. If you saw a good movie, then you enjoyed yourself. If possible, use the Law of Detachment to draw a conclusion. If not possible, write not possible. 3. If Robbie wants to save money to buy a car, he must get a part-time job. Robbie started a new job yesterday at a grocery store. Use the Law of Detachment and the Law of Syllogism to draw a conclusion. 4. If it is raining, the temperature is greater than 320F. If the temperature is greater than 320F, then it is not freezing outside. It is raining. 5. If you live in Providence, then you live in Rhode Island. If you live in Rhode Island, then you live in the smallest state in the United States. Shannon lives in Providence.