Logic Conclusion based on facts “If… then…” Conclusions based on observations and patterns “Conjecture” “Counterexample” will show a conjecture is false.

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Presentation transcript:

Logic Conclusion based on facts “If… then…” Conclusions based on observations and patterns “Conjecture” “Counterexample” will show a conjecture is false Deductive Reasoning Inductive Reasoning

“1” if Inductive Reasoning “2” if Deductive Reasoning For the past two weeks there have always been an even number of birds at your feeder. Today there will be an even number of birds at your feeder. 1

“1” if Inductive Reasoning “2” if Deductive Reasoning In the last week, whenever you walked out your door and saw your cat in the tree, it rained that afternoon. You saw your cat in the tree this morning. It will rain this afternoon. 1

“1” if Inductive Reasoning “2” if Deductive Reasoning The sum of two odd numbers is always an even number. The sum of 17 and 21 is even. 2

“1” if Inductive Reasoning “2” if Deductive Reasoning The last 10 times you pushed an odd- numbered button, a red light flashed. If you push the button “5”, a red light will flash. 1

“1” if Inductive Reasoning “2” if Deductive Reasoning If yesterday was Thursday, then tomorrow is Saturday. 2

Hypothesis Conclusion If tomorrow is Saturday, then yesterday was Thursday Converse

Is the converse true (touch your lips) or false (touch nose) If a number is divisible by two, then it is an even number

Is the converse true (touch your lips) or false (touch nose) If x = 5, then x 2 = 25 If false, give a counterexample. -5

Is the converse true (touch your lips) or false (touch nose) If a figure is a square, then it has 4 sides. If false, give a counterexample. Rectangle

Which is a counterexample to the conjecture If a>b and c>d, then ac > bd There is no counterexample. The conjecture is true.

Give a counterexample to the conjecture: The difference of two rational numbers is always less than at least one of the numbers. (for example, the difference of 9 and 2 is 7) 8 and -5

If it is not raining, Jack will walk the dog.

If it is not raining, Jerry will go swimming.

Problem Solving Strategy: Use Logical Reasoning To celebrate getting their drivers' licenses, Liz, Ann, and Phil borrowed their parents cars: a white sedan, a red sports car; and a red compact, (1) Phil's parents own only red cars. (2) Liz borrowed a red car, but her parents wouldn't let her drive their sports car. Who was driving which car?

Sports (Red) Sedan (White) Compact (Red) Liz Ann Phil

To celebrate getting their drivers' licenses, Liz, Ann, and Phil borrowed their parents cars: a white sedan, a red sports car; and a red compact, (1) Phil's parents own only red cars. (2) Liz borrowed a red car, but her parents wouldn't let her drive their sports car. Who was driving which car? Sports (Red) Sedan (White) Compact (Red) Liz Ann Phil X1X1

To celebrate getting their drivers' licenses, Liz, Ann, and Phil borrowed their parents cars: a white sedan, a red sports car; and a red compact, (1) Phil's parents own only red cars. (2) Liz borrowed a red car, but her parents wouldn't let her drive their sports car. Who was driving which car? Sports (Red) Sedan (White) Compact (Red) Liz Ann Phil X1X1 X2X2 X2X2 X2X2 X2X2

The houses on your street are numbered 1 to 120. No numbers are skipped. How many house numbers contain at least one digit 5?

Fundamental Counting Principle 1)How many locker combinations are possible on a standard lock with digits 0 – 49 using the right/left/right sequence if no number can be used more than once in the combination? 2)How many different phone numbers are possible in the 909 area code starting with 594? 594-__ __ __ __

Assignment: p ,3,6,7 We will review Wednesday and the Chapter Test is Friday