Reasoning Strategies Goal: To be able to identify a deductive or inductive reasoning strategy State the hypothesis and conclusion of deductive statements.

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Presentation transcript:

Reasoning Strategies Goal: To be able to identify a deductive or inductive reasoning strategy State the hypothesis and conclusion of deductive statements Write a converse Show a conterexample

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

The converse of a conditional statement can be found by interchanging the hypothesis and conclusion. The converse of a conditional statement may or may not be true

Counterexample One statement that proves the statement to be false All you need is one counterexample to prove something false

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.

Assignment Page 192 (1-5) all and Page 193 (1-5) all