To solve problems by looking for a pattern

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Presentation transcript:

To solve problems by looking for a pattern 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 Deductive reasoning- logical conclusions based on a general case

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

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

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 # Rays # angles 1 2 3 4 5 6 7 8 9 10 1 3 6 10 15 21 28 36 45

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

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

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.

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 P  R : A square is a parallelogram

Example: P  Q Q 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.

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 P

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