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2.3 Deductive Reasoning

2.3 Deductive Reasoning. Chapter 2: Reasoning and Proof. 2.3 Deductive Reasoning. Deductive Reasoning: Logical reasoning; reasoning from given statements to a conclusion. Inductive Reasoning: Based on patterns you observe. Many people use deductive reasoning in their jobs:

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2.3 Deductive Reasoning

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  1. 2.3 Deductive Reasoning Chapter 2: Reasoning and Proof

  2. 2.3 Deductive Reasoning Deductive Reasoning: Logical reasoning; reasoning from given statements to a conclusion Inductive Reasoning: Based on patterns you observe Many people use deductive reasoning in their jobs: A physician diagnosing a patient’s illness uses deductive reasoning. A carpenter uses deductive reasoning to determine what materials will be needed at a work site.

  3. Auto Maintenance An auto mechanic knows that if a car has a dead battery, the car will not start. A mechanic begins work on a car and finds the battery is dead. What conclusion can she make?

  4. Auto Maintenance Suppose that a mechanic begins work on a car and finds that the car will not start. Can the mechanic conclude that the car has a dead battery?

  5. Law of Detachment If a conditional is true and its hypothesis is true, then its conclusion is true. Symbolic form: If p -> q is a true statement and p is true, then q is true.

  6. Using the Law of Detachment For the given statements, what can you conclude? Given: If M is the midpoint of a segment, then it divides the segment into two congruent segments. M is the midpoint of AB

  7. Using the Law of Detachment 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?

  8. Real World Connection Does the following argument illustrate the Law of Detachment? Given: If it is snowing, then the temperature in less than or equal to 32°F. The temperature is 20°F. You conclude: It must be snowing. Can you make this conclusion?

  9. Can you use the Law of Detachment? Given: If a road is icy, then driving conditions are hazardous. Driving conditions are hazardous. Can you conclude that the road is icy?

  10. Law of Syllogism Allows you to state a conclusion from two true conditional statements when the conclusion of one statement is the hypothesis of the other statements. Symbolic Form: If p -> q and q -> r are true statements, then p -> r is a true statement.

  11. Using the Law of Syllogism Use the Law of Syllogism to draw a conclusion from the following true statements: If a number is prime, then it does not have repeated factors. If a number does not have repeated factors, then it is not a perfect square.

  12. Using the Law of Syllogism to state a conclusion: If a number ends in 0, then it is divisible by 10. If a number is divisible by 10, then it is divisible by 5. Conclusion: If a number ends in 6, then it is divisible by 2. If a number ends in 4, then it is divisible by 2. Conclusion:

  13. Real World Connection Use the Law of Detachment and the Law of Syllogism to draw conclusions from the following true statements: If a river is more than 4000 mi 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 4132 mi long. Conclusion:

  14. Real World Connection The Volga River is in Europe. If a river is less than 2300 mi long, it is not one of the world’s ten longest rivers. If a river is in Europe, then it is less than 2300 mi long. Conclusion:

  15. Homework • Pg 84 1-15

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