# Free Powerpoint Templates Page 2 Inductive Versus Deductive Reasoning

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• Free Powerpoint Templates Page 2
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• Inductive Versus Deductive Reasoning
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• Free Powerpoint Templates Page 4 Inductive Versus Deductive Reasoning There are two approaches to furthering knowledge 1.reasoning from known ideas and 2. synthesize observations.
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• Free Powerpoint Templates Page 5 Inductive Versus Deductive Reasoning In inductive reasoning you observe the world, and attempt to explain based on your observations. You start with no prior assumptions. Deductive reasoning consists of logical assertions from known facts.
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• 8-Aug-15 a.reaching a conclusion based on previous observation. b.It moves from the specific to the general Types of reasoning INDUCTIVE REASONING
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• 1 = 1 1 1 2 = 4 2 4 3 = 9 3 9 (-1) = 1 -1 1 BASED ON THE GIVEN EXAMPLES, DRAW A CONCLUSION/S.
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• 8-Aug-15 Examples 1 = 1 1 1 2 = 4 2 4 3 = 9 3 9 (-1) = 1 -1 1 Types of reasoning BASED ON THE EXAMPLES, WE NOTICED A PATTERN FROM WHICH WE DRAW A CONCLUSIONS.
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• 8-Aug-15 Examples 1 = 1 1 1 2 = 4 2 4 3 = 9 3 9 (-1) = 1 -1 1 Types of reasoning THROUGH INDUCTIVE REASONING, IT MAY BE CONCLUDED THAT WHENEVER A NUMBER IS SQUARED, THE RESULT IS A NUMBER WHICH IS GREATER THAN OR EQUAL TO THE ORIGINAL NUMBER.
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• 8-Aug-15 Examples 1 = 1 1 1 2 = 4 2 4 3 = 9 3 9 (-1) = 1 -1 1 Types of reasoning Inductive reasoning is making conclusions based on patterns you observe. The conclusion you reach is called a conjecture
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• 8-Aug-15 a.reaching a conclusion based on previous observation. Types of reasoning INDUCTIVE REASONING b. Conclusions are probably TRUE but not necessarily TRUE.
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• 8-Aug-15 2 = 4 2 4 3 = 9 3 9 (-1) = 1 -1 1 Consider this example () = > Does the conclusion hold true? Types of reasoning Conclusion: No. Because is greater than . WHENEVER A NUMBER IS SQUARED, THE RESULT IS A NUMBER WHICH IS GREATER THAN OR EQUAL TO THE ORIGINAL NUMBER.
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• 8-Aug-15 a.reaching a conclusion based on previous observation. Types of reasoning INDUCTIVE REASONING b. Conclusions are probably TRUE but not necessarily TRUE.
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• A BEGINNING OBSERVER OF AMERICAN BASEBALL MAY CONCLUDE, AFTER WATCHING SEVERAL GAMES, THAT THE GAME IS OVER AFTER 9 INNINGS. HE WILL ONLY REALIZE THAT THIS OBSERVATION IS FALSE AFTER OBSERVING A GAME WHICH IS TIED AFTER 9 INNINGS. Another example
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• 8-Aug-15 INDUCTIVE REASONING IS USEFUL BUT NOT CERTAIN. THERE WILL ALWAYS BE A CHANCE THAT THERE IS AN OBSERVATION THAT WILL SHOW THE REASONING TO BE FALSE. Types of reasoning INDUCTIVE REASONNG ONLY ONE OBSERVATION IS NEEDED TO PROVE THE CONCLUSION TO BE FALSE.
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• 8-Aug-15 Look carefully at the following figures. Then, use inductive reasoning to make a conjecture about the next figure in the pattern Types of reasoning If you have carefully observed the pattern, may be you came up with the figure below:
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• 8-Aug-15 Look at the patterns below. Can you draw the next figure or next set of dots using inductive reasoning? Types of reasoning The trick is to see that one dot is always placed between and above two dots. Also, the next figure always has one more dot at the very bottom row keeping this in mind, your next figure should look like this:
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• 8-Aug-15 Inductive reasoning is used often in life. Polling is an example of the use of inductive reasoning. If one were to poll one thousand people, and 300 of those people selected choice A, then one would infer that 30% of any population might also select choice A. This would be using inductive logic, because it does not definitively prove that 30% of any population would select choice A. Types of reasoning
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• 8-Aug-15 a.reaching a conclusion by combining known truths to create a new truth Types of reasoning DEDUCTIVE REASONNG b. deductive reasoning is certain, provided that the previously known truths are in fact true themselves.
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• 8-Aug-15 1. An angle is congruent to itself. Types of reasoning Examples 2. Mr. Samuel M. Gier is a math teacher. 3. If 2x = 8, then x = 4.
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• 8-Aug-15 Types of reasoning FORMS OF DEDUCTIVE REASONNG There are a few forms of deductive logic. One of the most common deductive logical arguments is modus ponens, which states that: p q read as If p, then q. p q read as p, therefore q
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• 8-Aug-15 If I stub my toe, then I will be in pain. I stub my toe. Therefore, I am in pain. Types of reasoning Example of modus ponens
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• 8-Aug-15 Types of reasoning FORMS OF DEDUCTIVE REASONNG Another form of deductive logic is modus tollens, which states the following. p q read as If p, then q. q p read as not q, therefore not p
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• 8-Aug-15 If today is Thursday, then the cafeteria will be serving burritos. The cafeteria is not serving burritos, therefore today is not Thursday. Types of reasoning Example of modus tollens
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• 8-Aug-15 Types of reasoning FORMS OF DEDUCTIVE REASONNG Another form of deductive logic is known as the If-Then Transitive Property. Simply put, it means that there can be chains of logic where one thing implies another thing. The If-Then Transitive Property states: p q read as If p, then q. (q r) (p r) read as ((If q, then r), therefore (if p, then r))
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• 8-Aug-15 If today is Thursday, then the cafeteria will be serving burritos. If the cafeteria will be serving burritos, then I will be happy. Therefore, if today is Thursday, then I will be happy. Types of reasoning Example of If-Then Transitive Property
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• 8-Aug-15 Deductive reasoning is based on laws or general principles. People using deductive reasoning apply a general principle to a specific example. Types of reasoning DEDUCTIVE REASONNG
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• 8-Aug-15 Use inductive reasoning to form arguments based on experience. Use deductive reasoning to form arguments based on rules or previously known facts. Types of reasoning Choosing a Strategy
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• 8-Aug-15 All vegetables are good for you. Broccoli is a vegetable. Therefore, broccoli is good for you. This is an example of what type of reasoning? Types of reasoning EXERCISES DEDUCTIVE REASONING
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• 8-Aug-15 Broccoli is a vegetable. Broccoli is a green. Therefore, all vegetables are green. Why is this conclusion invalid? Types of reasoning EXERCISES
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• PROOF
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• KINDS OF PROOF
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• HOMEWORK Give two examples using deductive and inductive reasoning. Write your answers in a paper (one-half crosswise)

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