Section 2-3 Deductive Reasoning. Types of Reasoning:

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Section 2-3 Deductive Reasoning

Types of Reasoning:

Inductive Reasoning Conclusion based on several past observations The conclusion is probably true, but not necessarily true

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

Deductive Reasoning Conclusion based on accepted statements Conclusion must be true if the hypotheses are true. Logical Argument (follows logical order)

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

Two laws of Deductive Reasoning:

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

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

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

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.