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Deductive Reasoning

Deductive Reasoning. 2-3. Deductive Reasoning. The process of reasoning logically from a given statement to a conclusion. Law of detachment – if a conditional’s hypothesis is true, then its conclusion is true If and p is true then so is q. Example 1.

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Deductive Reasoning

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  1. Deductive Reasoning 2-3

  2. Deductive Reasoning • The process of reasoning logically from a given statement to a conclusion. • Law of detachment – if a conditional’s hypothesis is true, then its conclusion is true • If and p is true then so is q.

  3. Example 1 • Suppose that a mechanic knows that if a car has a dead battery, the car will not start. A mechanic begins to work on a car and finds the battery is dead. What conclusion can she make?

  4. Example 2 • Given: If M is the midpoint of a segment, then it divides the segment into two congruent segments. • M is the midpoint of AB

  5. Example 3 • If a baseball player is a pitcher, then that player should not pitch a complete game two days in a row. Vladimir Nunez is a pitcher. On Monday, he pitches a complete game. What can you conclude?

  6. Example 4 • Does the following argument illustrate the Law of Detachment? • Given: If it is snowing, then the temperature is less than or equal to 32. The temperature is 20. • You conclude: It must be snowing.

  7. Example 5 • If possible use the Law of Detachment to draw a conclusion. If it is not possible explain why. • Given: If a road is icy, then driving conditions are hazardous. Driving conditions are hazardous.

  8. Law of Syllogism • Allows you to make conclusions about two different conditional statement when the conclusion of one is the hypothesis of the other. • If and and p is true, we can use the Law of Syllogism to say that r is also true

  9. Example 6 • If a number is prime, then it does not have any repeated factors. • If a number does not have any repeated factors, then it is not prime. • Draw a conclusion using the law of syllogism.

  10. Example 7 • If a number ends in 0 it is divisible by 10 • If a number is divisible by 10, then it is divisible by 5. • If possible, use the Law of Syllogism to draw a conclusion.

  11. Example 8 • If a number ends in 6, then it is divisible by 2. • If a number ends is 4, then it is divisible by 2. • If possible use the Law of Syllogism to to make a conclusion.

  12. Homework • Pg 85 #1-21, 27-32

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