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Unit 2.2 Notes

Unit 2.2 Notes. Deductive Reasoning. Vocabulary. Deductive reasoning Inductive reasoning Law of Detachment Law of Syllogism. What does p q mean?. It means if “hypothesis”, then “conclusion”. Another way to read p  q is "p implies q". Inductive Reasoning.

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Unit 2.2 Notes

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  1. Unit 2.2 Notes Deductive Reasoning

  2. Vocabulary Deductive reasoning Inductive reasoning Law of Detachment Law of Syllogism

  3. What does pq mean? It means if “hypothesis”, then “conclusion”. Another way to read pqis "p implies q".

  4. Inductive Reasoning Reasoning that is based on patterns you observe. 2, 4, 6, 8, …

  5. Deductive Reasoning The process of reasoning logically from given statements to a conclusion.

  6. Deductive Reasoning Example 1 An auto mechanic knows that if a car has a dead battery, then it will not start. The mechanic is working on a Camaro and discovers that it has a dead battery. What can the mechanic conclude?

  7. Deductive Reasoning Example 1 An auto mechanic knows that if a car has a dead battery, then it will not start. The mechanic is working on a Camaro and discovers that it has a dead battery. Conclude: The Camaro will not start.

  8. Deductive Reasoning Example 1 - Converse The mechanic is working on a Camaro and discovers that it will not start. Can the mechanic conclude the Camaro’s battery is dead? No, it could be any number of other problems.

  9. Law of Detachment If pq is a true statement and p is true, then q must be true.

  10. Law of Detachment Example 1 Given: lf M is the midpoint of a segment, then it divides the segment into two congruent segments. M is the midpoint of AB. What can we conclude?

  11. Law of Detachment Example 1 Given: lf M is the midpoint of a segment, then it divides the segment into two congruent segments. M is the midpoint of AB. Conclude: M divides the segment into two congruent segments, AM and MB

  12. Law of Detachment Example 2 Given: If a baseball player is a pitcher, then he 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 we conclude?

  13. Law of Detachment Example 2 Given: If a baseball player is a pitcher, then he should not pitch a complete game two days in a row. Vladimir Nunez is a pitcher. On Monday, he pitches a complete game. Vladimir should not pitch a complete game on Tuesday.

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

  15. Law of Detachment Does the following argument illustrate the Law of Detachment? Given: If it is snowing, then the temperature is less than or equal to 32F. The temperature is 20F. You conclude: It must be snowing. No. This statement is not true. Truth Value: False

  16. Law of Detachment If possible use the Law of Detachment to draw a conclusion. Given: If a road is icy, then the driving conditions are hazardous. Driving conditions are hazardous. Conclusion?

  17. Law of Detachment If possible use the Law of Detachment to draw a conclusion. Given: If a road is icy, then the driving conditions are hazardous. Driving conditions are hazardous. Conclusion? No conclusion. There are other reasons for hazardous driving conditions.

  18. Law of Syllogism lf pq and qr are true statements, then pr is a true statement.

  19. Law of Syllogism Example 1 lf a number is prime, then it does not have repeated factors. lf a number does not have repeated factors, then it is not a perfect square. What can we conclude?

  20. Law of Syllogism Example 1 lf a number is prime, then it does not have repeated factors. lf a number does not have repeated factors, then it is not a perfect square. Conclusion: If a number is prime, then it is not a perfect square.

  21. Law of Syllogism Example 2 lf a number ends in 0, then it is divisible by 10. lf a number is divisible by 10, then it is divisible by 5. What can we conclude?

  22. Law of Syllogism Example 2 lf a number ends in 0, then it is divisible by 10. lf a number is divisible by 10, then it is divisible by 5. Conclude: If a number ends in 0, then it is divisible by 5.

  23. Law of Syllogism Example 3 lf a number ends in 6, then it is divisible by 2. lf a number ends in 4, then it is divisible by 2. What can we conclude? Cannot conclude anything.

  24. Law of Syllogism Example 3-A lf a number ends in 6, then it is divisible by 2. lf a number is divisible by two, then it is even. What can we conclude? Conclude: If a number ends in 6, then it is even.

  25. Law of Syllogism Example 4 lf a river is more than 4000 mi long, then it is longer than the Amazon. lf a river is longer than the Amazon, then it is the longest river in the world. The Nile is 4132 miles long. What can we conclude?

  26. Law of Syllogism Example 4 lf a river is more than 4000 mi long, then it is longer than the Amazon. lf a river is longer than the Amazon, then it is the longest river in the world. The Nile is 4132 miles long. Conclude: The Nile is the longest river in the world.

  27. Properties of Equality

  28. Properties of Congruence

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