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Understanding Deductive Reasoning: Laws and Applications

This section focuses on deductive reasoning, emphasizing its foundational laws, such as the Law of Detachment and the Law of Syllogism. It discusses how deductive reasoning uses accepted facts and logic to deduce conclusions. By exploring various examples, such as relationships between angles and implications of actions, it illustrates how to apply logical reasoning to draw valid conclusions. A comprehensive review helps reinforce key concepts and enhances problem-solving skills in mathematical contexts.

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Understanding Deductive Reasoning: Laws and Applications

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  1. Section 2.3 – Apply Deductive Reasoning HW #9 pg. 90 #4-10, 12

  2. Deductive Reasoning • If Nathan is enrolled at Del Rio High School, then Nathan has an ID number. • Does Nathan have an ID number?

  3. Deductive Reasoning • Uses facts, definitions, accepted properties, and laws of logic to form a logical argument.

  4. Law of Detachment • If the hypothesis is true, then the conclusion must be true • Mary goes to the movies every Friday and Saturday night. Today is Friday. Is Mary going to the movies?

  5. Example • If two angles are right angles, then they are congruent. Angle C and D are right angles. What can you conclude?

  6. Law of Syllogism • Example • If Rick takes chemistry this year, then Jesse will be Rick’s lab partner. If Jesse is Rick’s lab partner, then Rick will pass chemistry. • How can we condense this?

  7. Example • Use the Law of Syllogism to write a new statement. • If Joe takes Geometry this year, then he will take Algebra II next year. If Joe takes Algebra II next year, then he will graduate.

  8. Review! • Two types of laws of logic: • Law of Detachment • Ex: If two segments have the same length, then they are congruent. You know that BC = XY (they have the same measure). • Law of Syllogism • If , then . If , then

  9. Which is Which?? • State the law of logic that is illustrated • If you get an A on your math test, then you can go to the movies. If you go to the movies, then you can watch your favorite actor. Conclusion: If you get an A on your math test, then you can watch your favorite actor. • If , then . The value of is . Conclusion:

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