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Chapter 3: Problem 6

Use Euler diagrams to determine whether each argument is valid or invalid. All humans are warm-blooded. No reptiles are warm-blooded. Therefore, no reptiles are human.

Short Answer

Expert verified
The argument is valid. According to the Euler diagrams representing the two given propositions, there is no intersection between the 'Reptiles' and 'Humans' sets. This validates the conclusion that 'No reptiles are human.'

Step by step solution

01

Define the sets

Firstly, define three sets: 'Humans', 'Warm-blooded' and 'Reptiles'.
02

Represent the first proposition

The proposition 'All humans are warm-blooded' implies that the 'Humans' set is a subset of the 'Warm-blooded' set. Draw the 'Humans' set within the 'Warm-blooded' set to represent this.
03

Represent the second proposition

The proposition 'No reptiles are warm-blooded' implies that the 'Reptiles' set doesn't overlap with the 'Warm-blooded' set. Draw this by placing 'Reptiles' set outside the 'Warm-blooded' set.
04

Combine the diagrams

Now, combine these two diagrams to represent the complete argument. The 'Humans' set is a subset of 'Warm-blooded' set, and the 'Reptiles' set doesn't overlap with 'Warm-blooded' or 'Humans'.
05

Analyze the conclusion

The conclusion 'No reptiles are human' can be tested by checking the diagram. There should be no overlap between the 'Reptiles' and 'Humans' sets. The diagram correctly shows that 'Reptiles' and 'Humans' do not intersect.

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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. $$ \begin{aligned} &p \rightarrow q \\ &\frac{q \rightarrow p}{\therefore p \wedge q} \end{aligned} $$

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