Applying Deductive Reasoning

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Presentation transcript:

Applying Deductive Reasoning Geometry 2.3 Applying Deductive Reasoning

Deductive reasoning verses Inductive Reasoning Uses facts definitions, accepted properties, and laws of logic to form a logical argument Inductive Specific patterns and examples to form a conjecture

Using the Laws of Logic Law of Detachment Law of Syllogism pq pq p is true therefore, q is true. Law of Syllogism pq qr, then pr. The Law of Syllogism is also known as the Transitive Property of Conditional Statements. The law does not say that p (the original condition or fact) is known to be true. It simply states that if we agree that the statement pq is true and the statement qr is true, then we must accept that the statement pr is true.

Law of Syllogism and Law of Detachment If I stay after school, then I will ride the bus. If I ride the bus, then I will get home after 4 p.m. If I get home after 4 p.m. then I will not get to watch Scooby- Doo. If I don’t get to watch Scooby-Doo, then I won’t get to see “those meddling kids”. Suppose I stay after school. What can you conclude? If you know I did not get to see “those meddling kids”. What can you conclude? What law does this illustrate?