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Deductive Reasoning

Deductive Reasoning. Geometry Honors. Vocabulary. Inductive Reasoning – reasoning based on observed patterns. Deductive Reasoning – reasoning based on given statements. Example of Deductive Reasoning.

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Deductive Reasoning

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  1. Deductive Reasoning Geometry Honors

  2. Vocabulary Inductive Reasoning – reasoning based on observed patterns. Deductive Reasoning – reasoning based on given statements.

  3. Example of Deductive Reasoning An auto mechanic knows that if a car has a dead battery, the car will not start. A mechanic finds that the battery is dead. What conclusion can he make? What if he discovers the car won’t start. Can he conclude that the car has a dead battery?

  4. Deductive Reasoning Law of Detachment– if a conditional statement is true, and its hypothesis is true, then it’s conclusion must be true. Example Utilizing the Law of Detachment If a student wants to go to college, then he/she must study hard. Joe wants to go to UCLA. What conclusion can you draw?

  5. Your turn The Law of Detachment A gardener knows that if it rains, the garden will be watered. It is raining. What conclusion can he make?

  6. Can you use the Law of Detachment to make the following conclusion? If you make a field goal in basketball, you score two points. Jenna scored two points. Therefore, you conclude Jenna made a field goal.

  7. Deductive Reasoning Law of Syllogism– if pq and qr are both true, then pr is also true. Example Utilizing the Law of Syllogism If a number ends in zero, then it is divisible by 10. If a number is divisible by 10, then it is divisible by 5. What true conclusion can you make?

  8. Your turn The Law of Syllogism If a quadrilateral is a square, then it contains four right angles. If a quadrilateral contains four right angles, then it is a rectangle. What conclusion can you draw?

  9. It is possible to use both Laws of Deductive Reasoning in the same situation. If a river is more than 4000 miles long, then it is longer than the Amazon. If a river is longer than the Amazon, then it is the longest river in the world. The Nile is 4,132 miles long. What conclusion can you draw?

  10. Law of Syllogism: If a river is more than 4000 miles long, then it is longer than the Amazon. If a river is longer than the Amazon, then it is the longest river in the world. Leads to … If a river is more than 4000 miles long, then it is the longest river in the world.

  11. Law of Detachment: If a river is more than 4000 miles long, then it is the longest river in the world. and The Nile is 4,132 miles long. Conclusion: The Nile is the longest river in the world.

  12. The Chain Rule and Symbols: The Chain Rule is used to combine two conditionals of the form pq and qr into pr.

  13. Chain Rule Example pq: If Jane leaves home late, then she will miss her train. qr: If Jane misses her train, then she will be late for work. CONCLUSION pr: If Jane leaves home late, then she will be late for work.

  14. Chain Rule Example pq: If you have a job, then you will get money. qr: If you have money, then you can buy food. CONCLUSION pr: If you have a job, the you can buy food.

  15. More Complex Chain Rule Examples ~ad c ~b a b ~da What conclusion can we draw? Now use the chain rule… We can start by writing the contrapositive of the first conditional (because they have the same truth value). ~da a b b ~c CONCLUSION: ~d ~c Now we need the contrapositive of c ~b… ~da

  16. Let’s do the Chain Rule Worksheet together.

  17. Draw a conclusion for the following: 1. If you are involved in extra-curricular activities, your school spirit increases. If your school spirit increases, then your grades improve.

  18. Draw a conclusion for the following: 2. p  q q  t r  p

  19. Draw a conclusion for the following: 3. ~x  y z  ~x y  ~t

  20. Draw a conclusion for the following: 4. ~x  z t  ~z ~t  r

  21. Draw a conclusion for the following: 5. a  b ~c  ~b ~a  e

  22. Draw a conclusion for the following: 6. e  b a  ~c ~e  c ~a  f

  23. Draw a conclusion for the following: 7. m  n t  ~n k  ~p ~m  p ~t  ~r

  24. HOMEWORK • Pg. 84: 1-15 • Logic Worksheet • Chain Rule WS #2 • Quiz 2.1-2.3 Fri.

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