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Chapter 3: Problem 9

Use Euler diagrams to determine whether each argument is valid or invalid. All professors are wise people. Some wise people are actors. Therefore, some professors are actors.

Short Answer

Expert verified
The argument is invalid as per the drawn Euler Diagram.

Step by step solution

01

Identify the Sets

In this exercise, there are three sets to consider which are Professors, Wise People, and Actors. Each of these sets will be represented by a circle in the Euler Diagram.
02

Draw the First Premise

The first premise says 'All professors are wise people'. This implies that the set of Professors is completely inside the set of Wise People. Therefore, one circle (Professors) is drawn inside the other (Wise people).
03

Draw the Second Premise

The second premise says 'Some wise people are actors'. This indicates that there is some overlap between the Wise People circle and the Actors circle. The circle for the Actors is drawn such that it intersects with the circle of the Wise people, but not necessarily with the circle of the Professors.
04

Interpret the Diagram in Light of the Conclusion

The argument concludes that 'Some professors are actors'. However, in the drawn diagram this conclusion is not necessarily true since the overlap between Professors and Actors is not guaranteed according to the premises. Thus, the argument is invalid.

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Most popular questions from this chapter

Translate each argument into symbolic form. Then determine whether the argument is valid or invalid. You may use a truth table or, if applicable, compare the argument's symbolic form to a standard valid or invalid form. (You can ignore differences in past, present, and future tense.) If a metrorail system is not in operation, there are traffic delays. Over the past year there have been no traffic delays. \(\therefore\) Over the past year a metrorail system has been in operation.

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Describe what is meant by a valid argument.

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