1. 2.3 Deductive reasoning
Brett Solberg AHS ’11-’12

2. Warm-up
Write the inverse and contrapositive to the following statement.
If your car runs out of oil, then your engine will overheat.

3. Quiz Review your notes for 1 minute.
Clear your desk of everything except a pencil.

4. Today’s Objectives Deductive Reasoning
Law of Detachment
Lay of Syllogism
Draw conclusions from given statements.

5. Reasoning Inductive Deductive
Reasoning based off of observable patterns.
Deductive
Reasoning logically from given facts to reach a conclusion.
Law of Detachment
Law of Syllogism

6. Law of Detachment
If a conditional is true, and the hypothesis is true, then the conclusion is true.
If p → q and p is true, than q is true.
If it snows on Saturday, then I will go snowboarding.

7. Example
A car will not start if the battery is dead. A mechanic finds out the battery in a car is dead. What can he conclude?
What if the mechanic doesn’t know if the battery is dead but the car will not start. Can he conclude that the battery is dead?

8. Law of Syllogism If p → q and q → r are true, then p → r.
All men are mortal.
I am a man.
I am mortal
Socrates

9. Example If you study, then you will get good grades.
If you get good grades, then your parents will be happy.
If you study,
then your parents will be happy.

10. Class Assignment
Worksheet 2-3