Earlier we learned about inductive reasoning. • Earlier we learned about inductive reasoning. • Look at specific examples. • Recognize patterns, which.

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Presentation transcript:

Earlier we learned about inductive reasoning. • Earlier we learned about inductive reasoning. • Look at specific examples. • Recognize patterns, which you assume will continue. • Use the examples to find a general rule.

Deductive Reasoning

Deductive Reasoning •. Start with general rules Deductive Reasoning • Start with general rules you know are always true.

Deductive Reasoning •. Start with general rules Deductive Reasoning • Start with general rules you know are always true. • Use those to prove a conclusion.

If you start with true statements, the conclusion you reach must also be true.

Among the rules we use for deductive reasoning are …

Law of Detachment •. If the hypothesis of a true Law of Detachment • If the hypothesis of a true conditional is true, then the conclusion must also be true. • If A  B and A, then B. • You know the “if”, so you can conclude the “then”.

•. If you’re in Algebra I one. year, then you should be in • If you’re in Algebra I one year, then you should be in Geometry the following year. • All of you were in Algebra I last year.

•. If you’re in Algebra I one. year, then you should be in • If you’re in Algebra I one year, then you should be in Geometry the following year. • All of you were in Algebra I last year. CONCLUSION: • You should be in Geometry this year.

•. You have to stop for gas when. you drive a long distance. •. Mr • You have to stop for gas when you drive a long distance. • Mr. Burrow drive a long distance to national quiz bowl last summer.

• So he had to stop for gas.

Law of Syllogism (also called “Transitive Law”) •. If A  B and B  C, Law of Syllogism (also called “Transitive Law”) • If A  B and B  C, then A  C • If one thing implies another and the second implies a third, then the first implies the third.

•. If you get an A on all your. tests, then you will get an • If you get an A on all your tests, then you will get an A in the class. • If you get an A in the class, then your parents will be happy.

•. If you get an A on all your. tests, then you will get an • If you get an A on all your tests, then you will get an A in the class. • If you get an A in the class, then your parents will be happy. CONCLUSION • If you get an A on all your tests, then your parents will be happy.

•. It is usually harder to use. deductive reasoning than • It is usually harder to use deductive reasoning than inductive reasoning, BUT the conclusion will always be true.

•. Deductive reasoning •. Law of Detachment • • Deductive reasoning • Law of Detachment • Law of Syllogism (Transitive)