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Finite Mathematics for the Managerial, Life, and Social Sciences: An Applied Approach
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Chapter APPXA / Exercise 5
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Chapter 12 1. Define “deductive reasoning” and “decision making.” How are they different? Describe “conditional reasoning” (or “propositional reasoning”). Provide an original example of conditional reasoning. Define “syllogism,” and provide an example. How are syllogisms different from conditional reasoning problems? Deductive reasoning: you begin with some specific premises that are true, and you need to judge whether those premises allow you to draw a particular conclusion, based on the principles of logic. You need to draw some logical conclusions, based on the information supplied to you. A deductive-reasoning task provides you with all the information you need to draw a conclusion. Furthermore, the premises are either true or false, and you must use the rules of formal logic in order to draw conclusions Decision making: we evaluate and choose among several alternatives; we often use three heuristics, or general strategies, to make decisions. You must assess the information and choose among two or more alternatives. Decision making is much more ambiguous then deductive reasoning. Information may be missing or contradictory and there is no clear-cut rules that tell us how to proceed from the information to the conclusions. You may never know whether your decision was correct, and you may need to take additional factors into account. Conditional reasoning task (also called a propositional reasoning task) describes the relationship between conditions. It is a kind of deductive reasoning task. For example; If rabies is contagious, then a dog that was bitten by a rabid racoon now has rabies. The dog has rabies. Therefore, this dog was bitten by a rabid racoon Syllogism consists of two statements that we must assume to be true, plus a conclusion. Syllogisms refer to quantities, so they use the words all, none, some, and other similar terms. For example: Some psychology majors are friendly people. Some friendly people are concerned about poverty. Therefore, some psychology majors are concerned about poverty. In a syllogism, you must judge whether the conclusion is valid, invalid, or indeterminate. Where as in a conditional reasoning task you must judge only if it is valid or invalid.
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Finite Mathematics for the Managerial, Life, and Social Sciences: An Applied Approach
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Chapter APPXA / Exercise 5
Finite Mathematics for the Managerial, Life, and Social Sciences: An Applied Approach
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2. Do Demonstration 12.1. Define the “propositional calculus.” Given the statement, “If it is sunny, then it must be hot,” specify the following types of conditional reasoning situations.
Which of the above will lead to a valid conclusion, and of those two, which is the most difficult to solve?

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