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Chapter 3: Problem 15

Use Euler diagrams to determine whether each argument is valid or invalid. All dancers are athletes. Savion Glover is an athlete. Therefore, Savion Glover is a dancer.

Short Answer

Expert verified
The argument 'All dancers are athletes. Savion Glover is an athlete. Therefore, Savion Glover is a dancer.' is invalid as demonstrated by the Euler diagram. Savion Glover is indeed an athlete, but cannot with certainty be identified as a dancer based on the given premises.

Step by step solution

01

- Draw the first Euler Diagram

Represent 'dancers' as a subset of 'athletes'. Draw a larger circle for athletes and within this circle, draw a smaller circle to represent dancers. This indicates the relationship that 'All dancers are athletes', which is the first premise.
02

- Place Savion Glover in the Diagram

According to the second premise, 'Savion Glover is an athlete', place him in the larger circle which represents athletes. However, it is not specified where exactly in the circle, so place Savion somewhere in the athlete's circle, but not necessarily in the dancer's circle.
03

- Evaluate the Conclusion

The conclusion states that 'Savion Glover is a dancer'. Looking at the Euler diagram, while it is true that Savion Glover is an athlete, he may or may not be a dancer, because the diagram allows for Savion to be an athlete who is not a dancer. Thus, the argument is invalid.

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Most popular questions from this chapter

Explain how to use Euler diagrams to determine whether or not an argument is valid.

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 it rains or snows, then I read. I am not reading. \(\therefore\) It is neither raining nor snowing.

Determine whether each argument is valid or invalid. No \(A\) are \(B\), some \(A\) are \(C\), and all \(C\) are \(D\). Thus, some \(D\) are \(C\).

This is an excerpt from a 1967 speech in the U.S. House of Representatives by Representative Adam Clayton Powell: He who is without sin should cast the first stone. There is no one here who does not have a skeleton in his closet. I know, and I know them by name. Powell's argument can be expressed as follows: No sinner is one who should cast the first stone. All people here are sinners. Therefore, no person here is one who should cast the first stone. Use an Euler diagram to determine whether the argument is valid or invalid.

Use a truth table to determine whether the symbolic form of the argument is valid or invalid. $$ \begin{aligned} &p \rightarrow q \\ &\underline{q \rightarrow r} \\ &\therefore r \rightarrow p \end{aligned} $$
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