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Logic & Reasoning Deductive Reasoning
Deductive Reasoning logically from given statements to a conclusion. n Think of building an argument “brick by brick”. n
Think of this reasoning like falling dominoes—one knocks over the next, which knocks over the next and so on.
Example argument If the defendant’s fingerprints are on the wrapper, then the defendant touched the wrapper.
If the defendant touched the wrapper, then the defendant took the candy.
If the defendant took the candy, then the defendant is guilty of stealing.
Conclusion… If the defendant’s fingerprints are on the wrapper, then the defendant is guilty of stealing ____________.
With this type of reasoning, one conjecture can lead to another, which leads to another, and so on.
Deductive reasoning If it is Friday, then I am happy If I am happy , then I jump up and down. Conclusion: If it is Friday, then I jump up and down.
Try this… If the calculator has no battery, then it is not working. If it is not working , then I cannot use it. Conclusion: If the calculator has no battery, I cannot use it. then _______________.
Deductive reasoning in literature
Faulty Reasoning 1. If a number ends in 6, then it is divisible by 2. 2. If a number ends in 0, then it is divisible by 2. Conclusion: None- the conclusion of the first statement is not the hypothesis of the second.
Is the conclusion valid? ? If the calculator is broken, then it is not working. n If the calculator has no battery, then it is not working. n Conclusion: If the calculator is broken, then it has no battery. Answer: Invalid, there could be another reason it is broken.
Another form of deductive reasoning
You can take apart a statement and fit it to a situation. You start by assuming the given statement is true.
Example If it is snowing, then we can stay home. (true) It is snowing. (situation) Conclusion: We can stay home.
Example If M is the midpoint of a segment, then it divides the segment into two congruent parts. (true) M is the midpoint of A Conclusion: M B
Example If it is snowing, then the temperature is less than 32º. (true) It is snowing. (situation) Conclusion: The temperature is less than 32º.
Valid or not? ? Jamal knows that if he misses the practice the day before a game, then he will not be a starting player in the game. Jamal misses practice on Tuesday, so he concludes that he will not be a starter for Wednesday’s game.
Valid or not? ? Sarah knows that all sophomores take driver’s education in her school. Bob takes driver’s education. Sara conlcudes that Bob is a sophomore.
INVALID n Just because he took driver’s education, it doesn’t mean he went to her school, so maybe he is a junior at another school.
Summary If I study, then I will earn a good grade. If I earn a good grade, then I can drive the car. Conclusion: __________ If I study, then I can drive the car.
Summary If it is Friday, then I am happy. It is Friday. I am happy Conclusion: _________. If it is Monday, then I am depressed. None. You might be Conclusion: _________. depressed for another reason.