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2.4 Deductive Reasoning

2.4 Deductive Reasoning. Deductive Reasoning – USES FACTS, RULES, DEFINITIONS AND PROPERTIES TO REACH A LOGICAL CONCLUSION. Deductive or Inductive?

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2.4 Deductive Reasoning

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  1. 2.4 Deductive Reasoning

  2. Deductive Reasoning – USES FACTS, RULES, DEFINITIONS AND PROPERTIES TO REACH A LOGICAL CONCLUSION • Deductive or Inductive? • 1.Every time Katie has worn her favorite socks to a softball game, she has gotten at least one hit. Katie is wearing her favorite socks to a game tonight, so she concludes that she will get at least one hit. • 2.Sandra learned that if it is cloudy at night it will not be as cold in the morning as it would be if there are no clouds at night. Sandra knows it will be cloudy tonight, so she believes it will not be cold tomorrow morning. • 3. IF John is late making his car insurance payment, he will be assessed a late fee of $50. John’s payment is late this month, so he concludes that he will be assessed a late fee of $50.

  3. INDUCTIVE REASONING • Only one counter example is needed to disprove DEDUCTIVE REASONING Used to prove a conjecture, not disprove

  4. Law of detachment • If p q is a true statement and p is true, then q is true. • p q If a car is out of gas, then it will not start • p; Sarah’s car is out of gas • q; Sarah’s car will not start

  5. DETERMINE WHETHER EACH CONCLUSION IS VALID BASED ON THE GIVEN INOFRMATION. • 1. If 3 points are noncollinear, they determine a plane. • Points A, B, and C lie in plane G. • Points A, B and C are noncollinear. • 2. If a student turns in a permission slip, then the student can go on the field trip. • Felipe turned in his permission slip. • Felipe can go on the field trip.

  6. Law of syllogism • Draws conclusion from two true conditional statements when conclusion of one is the hypothesis of the next • If p q and q r, then p r is true. • If you get a job, then you will earn money. • If you earn money, then you will buy a car. • If you get a job, then you will buy a car.

  7. Determine which statement follows logically from the given statements. • (1) If you do not get enough sleep, then you will be tired. • (2) If you are tired, then you will not do well on the test. • A. If you are tired, then you will not get enough sleep. • B. If you do not get enough sleep, then you will not do well on the test. • C. If you do not do well on the test, then you did not get enough sleep. • D. There is no valid conclusion.

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