2-4 Deductive Reasoning. Deductive Reasoning …(sometimes called Logical Reasoning) is the process of reasoning logically from given statements or facts.

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Presentation transcript:

2-4 Deductive Reasoning

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

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

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.

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

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.

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.

p. 110 #7 If a rectangle has side lengths 3 cm and 4 cm, then it has area 12 cm 2. Rectangle ABCD has area 12 cm 2. No conclusion is possible; the hypothesis has not been satisfied.

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. p. 110 #14