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2.3: Deductive Reasoning

2.3: Deductive Reasoning. p. 85-91. Deductive Reasoning. Use facts, definitions and accepted properties in logical order to write a logical argument. Law of Detachment. If p q is a true conditional statement and p is true, then q is true. Ex.

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2.3: Deductive Reasoning

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  1. 2.3: Deductive Reasoning p. 85-91

  2. Deductive Reasoning • Use facts, definitions and accepted properties in logical order to write a logical argument.

  3. Law of Detachment • If pq is a true conditional statement and p is true, then q is true. • Ex. • If I pass the test, then I get an A in geometry. (pq) • I passed the test.(p) • So I got an A in geometry.(q)

  4. Law of Syllogism • If pq and qr are true conditional statements, then p r is true. Ex. 1) If I pass the test, then I get an A in geometry. 2) If I get an A in geometry, then I get a new car. 3) I passed the test so I get a new car.

  5. Ex 1. Law of Detachment or Law of Syllogism or neither • 1. If an angle is acute, then it is not obtuse. • 2. <ABC is acute. • 3. <ABC is not obtuse. • Valid by Law of Detachment

  6. Ex 2. Law of Detachment or Law of Syllogism or neither • 1. Right angles are congruent. • 2. <A <B • 3. <A and <B are right angles. • Invalid. Statement 2 is not related to the hypothesis

  7. Ex 3.Law of Detachment or Law of Syllogism • 1. If you save a penny, then you have earned a penny. • 2. Art saves a penny. • 3. Art has earned a penny. • Valid by Law of Detachment.

  8. Ex 4. Law of Detachment or Law of Syllogism or neither • 1. If you are a teenager, then you are always right. • 2. If you are always right, then people will listen to you. • 3. If you are a teenager, then people will listen to you. • Valid by Law of Syllogism.

  9. Ex 5. Law of Detachment or Law of Syllogism • 1. If you drive 50 miles per hour in a school zone, then you will get a speeding ticket. • 2. Pat received a speeding ticket. • 3. Pat was driving 50 miles per hour in a school zone. • Invalid. Pat could have received a speeding ticket for speeding on the highway.

  10. For the following examples, write a conclusion using the true statements. If no conclusion is possible, write no conclusion. State the applicable law.

  11. Example 1 • If Jim gets stung by a bee, then he will get very ill. If he gets very ill, then he will go to the hospital. Jim gets stung by a bee. • Conclusion? • Jim will go to the hospital. • Law of Syllogism

  12. Example 2 • If two planes intersect, then their intersection is a line. Plane T and plane W intersect. • Conclusion? • Plane T and plane W intersect in a line. • Law of Detachment

  13. Example 3 • If you cut class, then you will receive ISS. You cut class. • Conclusion? • You received ISS. • Law of Detachment

  14. Example 4 • If Mike doesn’t work hard, then he won’t start the game and will quit the team. Mike quit the team. • Conclusion? • No conclusion. We do not why he quit the team.

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