Section 3.6 Euler Diagrams and Syllogistic Arguments

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Copyright 2013, 2010, 2007, Pearson, Education, Inc. Section 3.6 Euler Diagrams and Syllogistic Arguments

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Section 3.6 Euler Diagrams and Syllogistic Arguments. What You Will Learn. Euler diagrams Syllogistic arguments. Syllogistic Arguments. Another form of argument is called a syllogistic argument , better known as syllogism. - PowerPoint PPT Presentation

Transcript of Section 3.6 Euler Diagrams and Syllogistic Arguments

Page 1: Section 3.6 Euler Diagrams and Syllogistic Arguments

Copyright 2013, 2010, 2007, Pearson, Education, Inc.

Section 3.6

Euler Diagrams

and Syllogistic Arguments

Page 2: Section 3.6 Euler Diagrams and Syllogistic Arguments

Copyright 2013, 2010, 2007, Pearson, Education, Inc.

What You Will Learn

Euler diagrams

Syllogistic arguments

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Page 3: Section 3.6 Euler Diagrams and Syllogistic Arguments

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Syllogistic Arguments

Another form of argument is called a syllogistic argument, better known as syllogism.The validity of a syllogistic argument is determined by using Euler (pronounced “oiler”) diagrams.

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Euler Diagrams

One method used to determine whether an argument is valid or is a fallacy.Uses circles to represent sets in syllogistic arguments.

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Symbolic Arguments Versus Syllogistic Arguments

Euler diagramsall are, some are, none are, some are not

Syllogistic argument

Truth tables or by comparison with standard forms of arguments

and, or, not, if-then, if and only if

Symbolic argument

Methods of determining validity

Words or phrases used

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Example 3: Ballerinas and AthletesDetermine whether the following syllogism is valid or invalid.

All ballerinas are athletic.Keyshawn is athletic.∴ Keyshawn is a ballerina.

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Example 3: Ballerinas and AthletesSolution

Keyshawn is athletic, so must be placed in the set of athletic people, which is A. We have a choice, as shown above.

All ballerinas, B, are athletic, A.The conclusion does not necessarily

follow from the set of premises. The argument is invalid.3.6-7

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Example 4: Parrots and ChickensDetermine whether the following syllogism is valid or invalid.

No parrots eat chicken.Fletch does not eat chicken.∴ Fletch is a parrot.

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Example 4: Parrots and ChickensSolution

The first premise tells us that parrots and things that eat chicken are disjoint sets—that is, sets that do not intersect.Fletch is not a parrot, the argument is invalid, or is a fallacy.

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Example 5: A Syllogism Involving the Word SomeDetermine whether the following syllogism is valid or invalid.

All As are Bs.Some Bs are Cs.∴ Some As are Cs.

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Example 5: A Syllogism Involving the Word SomeSolutionThe premise “All As are Bs” is illustrated.

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Example 5: A Syllogism Involving the Word SomeSolutionThe premise “Some Bs are Cs” means that there is at least one B that is a C.

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Example 5: A Syllogism Involving the Word SomeSolutionThe first illustrations shows that the conclusion “Some As are Cs,” does not follow, the argument is invalid.

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Try This: p. 155 #11

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Example 6: Fish and Cows

Determine whether the following syllogism is valid or invalid.

No fish are mammals.All cows are mammals.∴ No fish are cows.

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Example 6: Fish and CowsSolutionThe first premise tells us that fish and mammals are disjoint sets. The second tells us that the set of cows is a subset of the set of mammals.The conclusion necessarily follows from the premises and the argument is valid.3.6-16

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Homework

p. 155 #9 – 27 (x3)

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