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Lesson 2.3 Notes DEDUCTIVE REASONING

BRING TEXTBOOKS TOMORROW!. EQ: How can I use deductive reasoning to make valid conclusion?. Lesson 2.3 Notes DEDUCTIVE REASONING. Mrs. Reese Geometry CP. Deductive Reasoning.

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Lesson 2.3 Notes DEDUCTIVE REASONING

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  1. BRING TEXTBOOKS TOMORROW! EQ: How can I use deductive reasoning to make valid conclusion? Lesson 2.3 NotesDEDUCTIVE REASONING Mrs. ReeseGeometry CP

  2. Deductive Reasoning • Deductive reasoning is the process of using facts, rules, definitions, and propertiesto reach a valid conclusion. • Different from inductive reasoning which uses observations and examples to form conjectures.

  3. Deductive Reasoning • In this lesson we use 2 Laws of Logic to make valid conclusions. • The Law of Detachment and • The Law of Syllogism

  4. Law of Detachment • If you have a true conditional statement… • If a student likes school, then he/she will get good grades. • and there is a specific case where the hypothesis is true… • Erica(a student) likes school. • then the conclusion must also be true! • Erica will get good grades.

  5. Law of Detachment (example 2) • If 2 angles are vertical, then they are congruent. • <1 and <2 are vertical angles. • Therefore… • <1 and <2 are congruent.

  6. Law of Detachment (example 3) • If a person likes to run, then he/she likes to exercise. • John likes to run. • Therefore… • John likes to exercise.

  7. Law of Syllogism This is called a Logical Chain • If you have a series of 2 or more logically linked true conditional statements… • If a student packs up before Mrs. Reese tells him, then he will be the last out of class. • If a student is last out of class, then he will be late to his next class. • If a student is late to class, then he will get detention. • You can write another true conditional statement as the conclusion, by combining the first hypothesis (if) and the last conclusion (then). • Therefore…If a student packs up before Mrs. Reese tells him, then he will get detention.

  8. Law of Syllogism (example 2)

  9. Law of Syllogism (example 3) If 2 angles are vertical, then they are congruent. If 2 angles are congruent, then they have the same measure. Therefore… If 2 angles are vertical, then they have the same measure.

  10. Invalid Conclusions If a student is sick, then he is absent. Jason is absent. Therefore…Jason is sick. INVALID example of the Law of Detachment because the second statement is based on the conclusion instead of the hypothesis of the original conditional statement.

  11. Invalid Conclusions If an animal is a bird, then it can fly. If an animal can fly, then it has wings. Therefore…If an animal has wings, then it is a bird. INVALID example of the Law of Syllogism because the third statement does not start with the first hypothesis.

  12. Classwork Lesson 2.3 Practice

  13. Lesson 2.3 Practice 1. If a person is in Mrs. Reese’s 6th period class, then the person is taking geometry. Timmy is in Mrs. Reese’s 6th period class. Therefore… Timmy is taking Geometry.

  14. Lesson 2.3 Practice 2. If a person scores 85-92 on a geometry test, then the person receives a B on the test. Christian scored 87 on the last geometry test. Therefore… Christian received a B on the test.

  15. Lesson 2.3 Practice 3. If you finish your chores on time, you may use the car tonight. You finish your chores on time. Therefore... You may use the car tonight.

  16. Lesson 2.3 Practice 4. If I go shopping, I will buy a new umbrella. If it rains on Saturday, then I am going shopping. If I buy a new umbrella, then I won’t get wet. Therefore… If it rains on Saturday, then I won’t get wet.

  17. Lesson 2.3 Practice 5. If it is warm, then it is spring. If flowers are blooming, then it is warm. If you see bees, then flowers are blooming. Therefore… If you see bees, then it is spring.

  18. Lesson 2.3 Practice 6. If school is canceled, then Jessica will stay home all day. If it snows in Greenville, then school is canceled. If Jessica stays home all day, then she will go on the internet. Therefore… If it snows in Greenville, then Jessica will go on the internet.

  19. Assignment Complete the back side of this worksheet. Look in magazines or sale papers and find examples of conditional statements. Bring in at least one example by Monday, October 3rd.

  20. Starter-page 91 #4-10 4. Identify the hypothesis and conclusion of the statementIf you’re there before it’s over, then you’re on time. 5. Write the converse of the statementIf it is raining, then there are clouds. 6. Write the inverse of the statementIf two lines are parallel, then they do not intersect. 7. Write the contrapositiveof the statement If a figure is a square, then it has four sides.

  21. Starter-page 91 #4-10 8. (1) If you’re not satisfied with a tape, then you can return it within a week for a full refund. (2) Yong is not satisfied with a tape. (3) Yong can return the tape within a week for a full refund. Law of Detachment Law of Syllogism No conclusion 9. (1) if x is a real number, then x is an integer. (2) x is an integer (3) x is a real number. Law of Detachment Law of Syllogism No conclusion

  22. Starter-page 91 #4-10 10. (1) If fossil fuels are burned, then acid rain is produced. (2) If acid rain is produced, then wildlife suffers. (3) If fossil fuels are burned, then wildlife suffers. Law of Detachment Law of Syllogism No conclusion

  23. Extra Examples Determine if a valid conclusion can be reached from the two true statements using the Law of Detachment or the Law of Syllogism. If a valid conclusion is possible, state it and the law that is used. If a valid conclusion does not follow, write no conclusion. If a number is a whole number, then it is an integer. If a number is an integer, then it is a rational number. Therefore… Law of Detachment Law of Syllogism No conclusion If a number is a whole number, then it is a rational number.

  24. Extra Examples If a dog eats Dogfood Delights, then the dog is happy. Fido is a happy dog! Therefore… Law of Detachment Law of Syllogism No conclusion NO CONCLUSION! • If two angles are complementary, then their measures have a sum of 90°. • <A and <B are complementary. • Therefore… • Law of Detachment Law of Syllogism No conclusion m<A + m<B = 90°

  25. Extra Examples If today is Friday, then we have a football game. If there is a pep rally, then today is Friday. Therefore… Law of Detachment Law of Syllogism No conclusion NO CONCLUSION! • If an animal is a fish, then it can swim. • Goldie can swim. • Therefore… • Law of Detachment Law of Syllogism No conclusion NO CONCLUSION!

  26. Extra Examples If today is Friday, then we take the Chapter 2 test on Monday. If we take the Chapter 2 test on Monday, then we take the definitions test on Tuesday. If we take the definitions test on Tuesday, then we will take the PSAT on Wednesday. If we take the PSAT on Wednesday, then we will not go to school on Thursday and Friday. If we don’t go to school on Thursday and Friday, then we will have a 4-day weekend! Therefore… If today is Friday, then we will have a 4-day weekend!

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