3.6

1. 3.6 Euler Diagrams and Syllogistic Arguments

2. 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.

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

4. Words or phrases used Methods of determining validity Symbolic argument and, or, not, if-then, if and only if Truth tables or by comparison with standard forms of arguments Syllogistic argument all are, some are, none are, some are not Euler diagrams Symbolic Arguments Versus Syllogistic Arguments

5. Example: Ballerinas and Athletes Determine whether the following syllogism is valid or invalid. All ballerinas are athletic. Keyshawn is athletic.  Keyshawn is a ballerina.

6. U U U A A A B B B Example: Ballerinas and Athletes All ballerinas, B, are athletic, A. Keyshawn is athletic, so must be placed in the set of athletic people, which is A. We have a choice, as shown above. The conclusion does not necessarily follow from the set of premises. The argument is invalid.

7. Ex. 2 All keys are made of brass. All things made of brass are valuable. Therefore, All keys are valuable. V B K The argument is valid because all of the keys are in the brass circle.

8. Read examples 4 – 6 P. 153-154

9. Homework • P. 155 # 7 – 27 all