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2.3 Using Deductive Reasoning to Verify Conjectures

2.3 Using Deductive Reasoning to Verify Conjectures. Deductive Reasoning When Alice meets the Pigeon in Wonderland, the Pigeon thinks she is a serpent. The pigeon reasons that serpents eat eggs, and Alice confirms that she has eaten eggs.

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2.3 Using Deductive Reasoning to Verify Conjectures

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  1. 2.3 Using Deductive Reasoning to Verify Conjectures Deductive Reasoning When Alice meets the Pigeon in Wonderland, the Pigeon thinks she is a serpent. The pigeon reasons that serpents eat eggs, and Alice confirms that she has eaten eggs. Alice: But I'm NOT a serpent, I tell you! I'm a -- I'm a --The Pigeon: Well! WHAT are you? I can see you're trying to invent something!Alice: I -- I'm a little girl. The Pigeon: A likely story indeed! I've seen a good many little girls in my time, but never ONE with such a neck as that! No, no! You're a serpent; and there's no use denying it. I suppose you'll be telling me next that you never tasted an egg!

  2. Laws of Logic The Law of Detachment- If the hypothesis of a true conditional statement is true, then the conclusion is also true. Example: If Ms. Curtis goes to the football game, then she will buy popcorn. Ms. Curtis goes to the football game. Therefore she will buy popcorn.

  3. Law of Syllogism- If hypothesis p, then conclusion q. If hypothesis q, then conclusion r. If hypothesis p, then conclusion r. Example: If you get a 90% on your test, then you get an A. If you get an A, then your parents will give you $20. If you get a 90% on your test, your parents will give you $20.

  4. Example 1 Determine if the conjecture is valid by the Law of Detachment. Given: If the side lengths of a triangle are 5 cm, 12 cm, and 13 cm, then the area of the triangle is 30 cm². The area of ∆PQR is 30 cm². Conjecture: ∆PQR has side lengths of 5 cm, 12 cm, and 13 cm.

  5. Example 2 Determine if the conjecture is valid by the Law of Detachment. Given: If a student passes his classes, then the student is eligible to play sports. Ross passed his classes. Conjecture: Ross is eligible to play sports.

  6. Example 3 Determine if the conjecture is valid by Law of Syllogism. Given: If a figure is a kite, then it is a quadrilateral. If a figure is a quadrilateral, then it is a polygon. Conjecture: If a figure is a kite, then it is a polygon. .

  7. Example 4 Determine if the conjecture is valid by Law of Syllogism. Given: If a number is divisible by 2, then it is even. If a number is even, then it is an integer. Conjecture: If a number is an integer, then it is divisible by 2.

  8. Example 5 Draw a conclusion from the given information. Given: If n > 2, then n + 4 > 6. n > 2 Conclusion:

  9. Example 6 Draw a conclusion from the given information. Given: If a polygon ABC is a triangle, then it has 3 sides. Polygon ABC is a triangle. Conclusion:

  10. Example 7 Write the statement the follows from the pair of statements given. If you work hard, then you get good grades. If you get good grades, you can play sports.

  11. Example 8 Write the statement the follows from the pair of statements given. If A is an even number, then A is divisible by 2. If A is divisible by 2 then it is also divisible by 1.

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