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2.3 Deductive Reasoning

2.3 Deductive Reasoning. OBJ: To use the Law of Detachment & the Law of Syllogism in deductive reasoning To solve problems by looking for a pattern. Inductive vs. Deductive Reasoning. Inductive reasoning- logical conclusions based on several observations

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2.3 Deductive Reasoning

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  1. 2.3 Deductive Reasoning OBJ: To use the Law of Detachment & the Law of Syllogism in deductive reasoning To solve problems by looking for a pattern

  2. Inductive vs. Deductive Reasoning • Inductive reasoning- logical conclusions based on several observations • Deductive reasoning- logical conclusions based on a general case

  3. Activity 1: • Pick a # • Add 5 • Double the result • Subtract 4 • Divide in half • Subtract the # started w/ • What’s your end result?

  4. Activity 2: Follow directions from activity 1 • Pick a # • Add 5 • Double • Subtract 4 • Divide in half • Subtract 1st # • N • N + 5 • 2(N + 5) = 2 N + 10 • 2 N + 6 • N + 3 • 3

  5. # Rays # angles Looking For A Pattern Find the # of angles formed by 10 distinct rays. There are many possibilities so let’s work a few and then see if we can develop a pattern 1 2 3 4 5 6 7 8 9 10 0 1 3 6 10 15 21 28 36 45

  6. P  Q P is true Q is true Therefore, Law of Detachment If P  Q is a true conditional and P is true, then Q is true.

  7. P  Q Q  R P  R Law of Syllogism If P  Q, Q  R are true conditionals, then P  R is also true.

  8. Example: If 2 #’s are odd, then the sum is even is a true conditional, and 3 and 5 are odd #’s. Use the law of detachment to reach a logical conclusion. • P : 2 #’s are odd • Q : sum is even • P is true because 3 and 5 are odd • Therefore, the sum of 3 and 5 is even.

  9. P  R : A square is a parallelogram Example: If a polygon is a square, then it is a rectangle. If a polygon is a rectangle, then it is a parallelogram. Use the law of syllogism to reach a logical conclusion. P  Q : Poly is a square rectangle Q  R : Poly is a rectangle  parallelogram

  10. Example: • IS THE STATEMENT VALID OR NOT? • (valid means it follows either one of the law forms) • If I watch TV, then I will not do my homework and I did my homework. P  Q Q Invalid. The format is detachment, and it doesn’t fit.

  11. P Your Turn: • Is this statement valid? • If a # is a multiple of 20, then it is a multiple of 5. Sam’s locker # is a multiple of 5. Therefore, Sam’s locker is a multiple of 20. P  Q INVALID Q

  12. Homework: • Put this in your agenda • Pg 90 1 - 15

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