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Chapter 3: Problem 13

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

Short Answer

Expert verified
The argument is valid because according to the Euler diagram, the conclusion logically follows from the premises. Savion Glover, as a dancer, is also an athlete.

Step by step solution

01

Identify The Statements

In this problem, there are two premises and a conclusion. The first premise is 'All dancers are athletes', the second premise is 'Savion Glover is a dancer', and the conclusion is 'Therefore, Savion Glover is an athlete.'.
02

Draw The Diagram For The Universal Proposition

For the universal categorical proposition 'All dancers are athletes', draw one circle within another. Label the inner circle as 'Dancers' and the outer circle as 'Athletes'. The inner circle represents the set of all dancers and the outer circle represents the set of all athletes. This indicates that all dancers are contained within the set of athletes.
03

Draw The Individual Savion Glover

For the particular proposition 'Savion Glover is a dancer', mark a point within the Dancers circle and label it 'Savion Glover'. This represents Savion Glover as an individual within the set of dancers and thereby within the set of athletes.
04

Determine If The Conclusion Follows

According to the diagram, the point representing Savion Glover falls within both the 'Dancers' circle and the 'Athletes' circle. Therefore, it can be inferred from the diagram that 'Savion Glover is an athlete' which is our conclusion, hence it follows logically and the argument is valid.

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Most popular questions from this chapter

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

Under what circumstances should Euler diagrams rather than truth tables be used to determine whether or not an argument is valid?

No animals that eat meat are vegetarians. No cat is a vegetarian. Felix is a cat. Therefore,,\(.\) a. Felix is a vegetarian. b. Felix is not a vegetarian. c. Felix eats meat. d. All animals that do not eat meat are vegetarians.

Use Euler diagrams to determine whether each argument is valid or invalid. All thefts are immoral acts. Some thefts are justifiable. Therefore, some immoral acts are justifiable.

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