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

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Presentation transcript:

2.3 Deductive reasoning Brett Solberg AHS ’11-’12

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

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

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

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 http://www.youtube.com/watch?v=ElH3aVXLZoo

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.

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?

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

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.

Class Assignment Worksheet 2-3