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2.3 Apply Deductive Reasoning

Learn about deductive reasoning and how to use it to arrive at a true conclusion. Explore examples and understand the process of logical inference.

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2.3 Apply Deductive Reasoning

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  1. 2.3 Apply Deductive Reasoning Objectives: • To recognize deductive reasoning and use it to arrive at a true conclusion.

  2. Example 2 In the Sudoku puzzle shown, what number must be written in the blue box? Why? ?

  3. Deductive Reasoning The process of demonstrating that if certain statements are accepted as true, then other statements can be shown to follow from them.

  4. Deductive Reasoning The “accepted” statements are sometimes premises or assumptions, and all deductive arguments must have them. Deductive reasoning uses logical inference to build on these assumptions. Unlike inductive reasoning, deductive reasoning will always lead to the truth as long as the assumptions are true.

  5. Example 2 All humans have skeletons is a reasonable assumption. So, since Mrs. DeZeeuw is a human, what must be true about her?

  6. Deductive Reasoning Deductive Reasoning General Specific

  7. Inductive vs. Deductive • We use inductive reasoning to investigate and discover things about our world. • Since the conjectures we make using our inductive reasoning are based on our fallible observation skills, we can be wrong. • We can search for a counterexample to disprove our conjectures. • In mathematics, we use our deductive reasoning to prove our conjectures beyond all uncertainty.

  8. Example 4 Follow along as with an excerpt from The Adventure of the Dancing Men by Sir Arthur Conan Doyle, paying particular attention to the deductions made by Sherlock Holmes. Click here

  9. Flavors of Deductive Reasoning Deductive reasoning comes in a variety of flavors: • Law of Detachment • Denying the Consequent • Law of Syllogism

  10. Law of Detachment

  11. Denying the Consequent

  12. Law of Syllogism

  13. Example 5 Use one of the laws of deductive reasoning to make a valid conclusion. If two segments have the same length, then they are congruent. You know that BC = XY. Law of Detachment

  14. Example 6 Use one of the laws of deductive reasoning to make a valid conclusion. If x > 5, then x2 > 25. If x2 > 25, then x2 > 20. Therefore, x>5 so x2>20 Law of Syllogism

  15. Example 7 Use one of the laws of deductive reasoning to make a valid conclusion. If a polygon is regular, then it is both equilateral and equiangular. Pentagon ABCDE is not equilateral or equiangular. Denying the Consequent

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