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2-4 Deductive Reasoning

2-4 Deductive Reasoning. …(sometimes called Logical Reasoning) is the process of reasoning logically from given statements or facts to a conclusion. Deductive Reasoning. If p  q is true and p is true, then q is true. Law of Detachment. Example of Law of Detachment:

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2-4 Deductive Reasoning

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  1. 2-4 Deductive Reasoning

  2. …(sometimes called Logical Reasoning) is the process of reasoning logically from given statements or facts to a conclusion Deductive Reasoning

  3. If pq is true and p is true, then q is true. Law of Detachment

  4. Example of Law of Detachment: If a student gets an A on a final exam, then the student will pass the course. Felicia got an A on her history final exam. Conclusion: Felicia will pass her history course.

  5. If pq is true qr is true, then pr is true. Law of Syllogism

  6. Example of Law of Syllogism: If a figure is a square, then the figure is a rectangle. If a figure is a rectangle, then the figure has four sides. Conclusion: If a figure is a square, then the figure has four sides.

  7. p. 110 #6 • If a doctor suspects her patient has a broken bone, then she should take an x-ray. • Dr. Ngemba suspects Lilly has a broken arm. • Dr. Ngemba should take an x-ray.

  8. p. 110 #7 • If a rectangle has side lengths 3 cm and 4 cm, then it has area 12 cm2. • Rectangle ABCD has area 12 cm2. • No conclusion is possible; the hypothesis has not been satisfied.

  9. p. 110 #14 • If you improve your vocabulary, then you will improve your score on a standardized test. • If you read often, then you will improve your vocabulary. • If you read often, then you will improve your score on a standardized test.

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