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Chapter 3: Problem 8

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

Short Answer

Expert verified
Based on the Euler diagram based on the given premises, the argument 'All humans are warm-blooded. No reptiles are human. Therefore, no reptiles are warm-blooded' is invalid.

Step by step solution

01

Identify the Premises and Conclusion

The first step in solving this exercise is to identify the premises and conclusion of the argument. Here, the two premises are: 'All humans are warm-blooded', 'No reptiles are human'. The conclusion is 'Therefore, no reptiles are warm-blooded'.
02

Draw the Euler Diagram for the Premises

An Euler diagram represents each premise with a shape; the overlap (or lack of overlap) between shapes illustrates the logical relationships between the premises. Start by drawing a circle to represent 'warm-blooded beings', and another to represent 'humans'. Since all humans are warm-blooded, the 'humans' circle falls entirely inside the 'warm-blooded beings' circle. Now, draw a third circle for 'reptiles'. As no reptiles are human, the 'reptiles' circle should be separate from the 'humans' circle. After this step, this would result in two circles ('warm-blooded beings' and 'reptiles') having no overlapping sections.
03

Evaluate the Conclusion Against the Diagram

The conclusion states 'no reptiles are warm-blooded'. In the Euler diagram, the circles for 'reptiles' and 'warm-blooded beings' do not overlap, but this does not confirm the conclusion that 'no reptiles are warm-blooded'. The fact that the 'reptiles' circle does not overlap with the 'humans' circle does not implicitly mean that it cannot overlap with the 'warm-blooded beings' circle. Therefore, based on this diagram, the argument is invalid.

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Most popular questions from this chapter

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I can't use Euler diagrams to determine the validity of an argument if one of the premises is false.

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 I'm at the beach, then I swim in the ocean. If I swim in the ocean, then I feel refreshed. \(\therefore\) If I'm not at the beach, then I don't feel refreshed.

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.) He is intelligent or an overachiever. He is not intelligent. \(\therefore\) He is an overachiever.

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 some journalists learn about the invasion, the newspapers will print the news. If the newspapers print the news, the invasion will not be a secret. The invasion was a secret. \(\therefore\) No journalists learned about the invasion.

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