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Section 3-6

Learn about the types of reasoning - inductive and deductive - to draw logical conclusions based on observations and accepted statements. Explore inductive reasoning using past observations and inductive reasoning with accepted statements.

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Section 3-6

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  1. Section 3-6 Inductive Reasoning

  2. Types of Reasoning:

  3. Inductive Reasoning • Conclusion based on several past observations • The conclusion is probably true, but not necessarily true • Uses words like noticed and observed

  4. Example: • For 3 weeks, the cafeteria served pizza on Wednesday. I conclude that next Wednesday the cafeteria will have pizza.

  5. Deductive Reasoning • Conclusion based on accepted statements: • Definitions, postulates, previous theorems, corollaries and given information

  6. Conclusion must be true if the hypotheses are true. • Logical Argument (follows logical order)

  7. Example: • Dictionaries are useful books. • Useful books are valuable. • Therefore, dictionaries are valuable.

  8. Two laws of Deductive Reasoning:

  9. Law of Detachment • If p  q is a true conditional statement and p is true, then q is true. 2 pieces of information: p and q

  10. Example: • If I pass the test, then I get an A in geometry. I passed the test. I get an A in Geometry.

  11. Law of syllogism • If p  q and q  r are true conditional statements, then p  r is true. • Similar to the Transitive property in algebra 3 pieces of information: p, q and r

  12. Example: • If people live in Manhattan, then they live in New York. • If people live in New York, then they live in the United States. • If people live in Manhattan, then they live in the United States.

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