1. Deductive Reasoning 2-3

2. Deductive Reasoning

3. Example 1  Suppose that a mechanic knows that if a car has a dead battery, the car will not start. A mechanic begins to work on a car and finds the battery is dead. What conclusion can she make?

4. Example 2  Given: If M is the midpoint of a segment, then it divides the segment into two congruent segments.  M is the midpoint of AB

5. Example 3  If a baseball player is a pitcher, then that player should not pitch a complete game two days in a row. Vladimir Nunez is a pitcher. On Monday, he pitches a complete game. What can you conclude?

6. Example 4

7. Example 5  If possible use the Law of Detachment to draw a conclusion. If it is not possible explain why.  Given: If a road is icy, then driving conditions are hazardous. Driving conditions are hazardous.

8. Law of Syllogism

9. Example 6  If a number is prime, then it does not have any repeated factors.  If a number does not have any repeated factors, then it is not prime.  Draw a conclusion using the law of syllogism.

10. Example 7  If a number ends in 0 it is divisible by 10  If a number is divisible by 10, then it is divisible by 5.  If possible, use the Law of Syllogism to draw a conclusion.

11. Example 8  If a number ends in 6, then it is divisible by 2.  If a number ends is 4, then it is divisible by 2.  If possible use the Law of Syllogism to to make a conclusion.

12. Homework  Pg 85 #1-21, 27-32