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## Deductive Reasoning

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**Deductive reasoning is the process of reasoning logically**from given statements to a conclusion.**Deductive Reasoning Is…**• Deductive reasoning is when you start from things you assume to be true, and draw conclusions that must be true if your assumptions are true. For Example All dogs have a tail. Buddy is a dog. Therefore Buddy has a tail.**Deductive Vs. Inductive**• Induction is usually described as moving from the specific to the general, while deduction begins with the general and ends with the specific. • Arguments based on laws, rules and accepted principles are generally used for Deductive Reasoning. Observations tend to be used for Inductive Arguments.**Still don’t get it?**• Man approaches to greet a new neighbor who is just moving into the house next door and asks what he does for a living. • Neighbor 1: I am a professor at the University, I teach deductive reasoning. • Man: Deductive reasoning? What is that? • Neighbor 1: Let me give you an example. I see you have a dog house out back. By that I deduce that you have a dog. • Man: That's right. • Neighbor 1: The fact that you have a dog, leads me to deduce that you have a family. • Man: Right again. • Neighbor 1: Since you have a family I deduce that you have a wife. • Man: Correct. • Neighbor 1: And since you have a wife, I can deduce that you are heterosexual. • Man: Yup. Neighbor 1: That is deductive reasoning!**Sherlock Holmes**• Sherlock Holmes would use deductive reasoning to help solve crimes. Example: Sherlock Holmes could help solve a mystery by making inferences. If Holmes saw a pack of cigarettes by a victim (the victim did not smoke), Holmes can make the assumption that the killer is a smoker. Andrew Ault**However…**• Deductive reasoning may not be the most accurate way of solving a problem, cause we all know that assumptions can be wrong.**Other faults of deductive reasoning**All Graduates of M.I.T. are Engineers George is not from M.I.T. Therefore George is not an Engineer Everybody from Texas is a cowboy Scott is from Texas Scott is a cowboy My sociology teacher told us that those of us who grew up in America in the twentieth century, with all of its greed, bigotry, and abuse of power inherited a sickness. Well, if I’m sick, I guess I don’t have to go to school today.**How Can Deductive Reasoning Be Applied In School?**“Ugggh, I don’t know…”**Science**Using laws and rules to make assumptions The law of gravity means everything that goes up must come downI threw a baseball in the airThat means the baseball must come down. Social Studies To be elected President you must obtain at least 270 electoral votesGeorge Bush won 287 electoral votesTherefore George Bush is the President.**Math**Scott has a case of soda in his house since there are 13 cans of soda left I deduce that Scott has drank 11 cans of soda. English When I see like in a sentence, I deduce that it is a simile.**What professions do you think commonly use Deductive**Reasoning?**Doctors**Journalists And many more... Lawyers Detectives**Why?**• These professions tend to ask a lot of questions to try to solve problems or to prove a point. • Often they would have to make assumptions to solve problems. • They would use rules and widely accepted beliefs to prove their argument. For example: An attorney states that his client is innocent because the crime victim was hit by a car. Since his client does not have a license. He can deduce that his client is innocent.**An auto mechanic knows that if a car has a dead battery, the**car will not start. A mechanic begins work on a car and finds the battery is dead. What conclusion will she make? The mechanic can conclude that the car will not start.**If there is lightning, then it is not safe to be out in the**open. Marla sees lightning from the soccer field. It is not safe for Marla to be out in the open.**If it is snowing, then the temperature is less than or equal**to 32˚F. The temperature is 20˚F. The converse of the original assumption is not true, so It is not possible to conclude that it is snowing.**If a baseball player is a pitcher, then that player should**not pitch a complete game two days in a row. Brent is a pitcher. On Monday, he pitches a complete game. What can you conclude?**Brent either did not pitch a complete game on Sunday or he**should not pitch a complete game on Tuesday.**If M is the midpoint of a segment, then it divides the**segment into two congruent segments. M is the midpoint of . You can conclude that M divides into two congruent segments, or**If an angle is obtuse, then it is not acute.**is not obtuse. The converse of the assumption is not true, so It is not possible to conclude that is acute.**If a road is icy, then driving conditions are hazardous.**Driving conditions are hazardous. The converse of the assumption is not true, so It is not possible to conclude that the road is icy.**bulbs**There are three switches downstairs. Each corresponds to one of the three light bulbs in the attic. You can turn the switches on and off and leave them in any position. How would you identify which switch corresponds to which light bulb, if you are only allowed one trip upstairs?**Answer**Turn one light switch one. Wait about 20 minutes, then turn it off. Turn another light on, and proceed upstairs. One light should be on, Two lights are off- however, one light is hot and one is cold.