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Chapter 2.4

Chapter 2.4. Deductive Reasoning. Objective: Be able to use the Law of Detachment and Syllogism. Glossary Section. Statement. Sentence that is either true or false but not both. Deductive Reasoning.

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Chapter 2.4

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  1. Chapter 2.4 Deductive Reasoning Objective: Be able to use the Law of Detachment and Syllogism.

  2. Glossary Section Statement Sentence that is either true or false but not both

  3. Deductive Reasoning • Deduction, starts with a general case and deduces specific instances. Deduction is used by scientists who take a general scientific law and apply it to a certain case. • Deductive reasoning is the process by which a person makes conclusions based on previously known facts. • Inductive Reasoning, examples or patterns • Deductive Reasoning, uses facts, rules or properties.

  4. Inductive and Deductive Reasoning A. WEATHER Determine whether the conclusion is based on inductive or deductive reasoning. In Miguel’s town, the month of April has had the most rain for the past 5 years. He thinks that April will have the most rain this year. Answer: Miguel’s conclusion is based on a pattern of observation, so he is using inductive reasoning.

  5. Inductive and Deductive Reasoning B. WEATHER Determine whether the conclusion is based on inductive or deductive reasoning. Sandra learned that if it is cloudy at night it will not be as cold in the morning than if there are no clouds at night. Sandra knows it will be cloudy tonight, so she believes it will not be cold tomorrow morning. Answer: Sandra is using facts that she has learned about clouds and temperature, so she is using deductive reasoning.

  6. Example Deductive Reasoning • Example. A tourist who visited Kingston met a number of people who were relaxed and laid back. The tourist concluded that all people in Kingston were relaxed and laid back. What reasoning process led to this conclusion? • Example. The last six times I went to Wal-Mart, the traffic was light on Wednesdays and heavy on Sundays. My conclusion is that weekdays have lighter traffic than weekends. What reasoning process led to this conclusion?

  7. Law of Syllogism • If p q is true, and qr is true, then p r is also true [(p q)(q r)]  (p r) Given: The symbol of a substance is Pb, then it is lead Given: The atomic number of lead is 82 Conclusion: If the symbol of a substance is Pb, the atomic number is 82.

  8. Law of Detachment • If p q is true, and p is true, then q is also true (If p then q) [(p q)p] q Given: BD bisects ABC Conclusion: ABD  CBD A D B C

  9. Use the Law of Detachment Determine whether the conclusion is valid based on the given information. If not, write invalid. Explain your reasoning.Given: If a figure is a square, then it is a parallelogram. The figure is a parallelogram.Conclusion: The figure is a square. Step 1 Identify the hypothesis p and the conclusion q of the true conditional. p: A figure is a square. q: The figure is a parallelogram.

  10. Use the Law of Detachment Step 2 Analyze the conclusion. The given statement the figure is a parallelogram satisfies the conclusion q of the true conditional. However, knowing that a conditional statement and its conclusion are true does not make the hypothesis true. The figure could be a rectangle. Answer: The conclusion is invalid.

  11. Analyze Conclusions • Given: 1. Vertical angles are congruent • 2. If two angles are congruent, then their measures are equal • Conclusion: If two angels are vertical, then their measures are equal. • Given: 1. If a figure is a square, then it is a polygon • 2. Figure A is a polygon. • Conclusion: Figure A is a square

  12. Determine whether the conclusion is valid based on the given information. If not, write invalid. Use a Venn diagram to help you.Given: If a figure is a square, then it has 4 right angles. A figure has 4 right angles.Conclusion: The figure is a square. A. valid B. invalid

  13. Practice Assignment • Page 121, 24-42 Even

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