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Chapter 3: Problem 10

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

Short Answer

Expert verified
The argument is invalid.

Step by step solution

01

Understand and Draw the Premises

First, we would draw two circles, one for comedians and one for funny people such that the entire comedians鈥� circle is inside the funny people鈥檚 circle, representing the idea that 'All comedians are funny people'. The second premise is 'Some funny people are professors'. To represent this, we would have another circle overlapping the funny people's circle, but not necessarily the comedians鈥� circle. This represents some funny people--those in the overlap of funny people and professors' circles--are professors.
02

Check the Validity of the Conclusion

The conclusion of the argument is that some comedians are professors, i.e., the comedians' circle (or part of it) should overlap with the professors' circle. However, based on the diagram that represents the premises, it is clear there is no mandatory overlap between the comedians and professors. The professors' circle might overlap with the comedians, but it might also only overlap with funny people who are not comedians.
03

Final Assessment

If the representation of the conclusion is not achieved by the representation of the premises, we can conclude that the argument is invalid. In this case, the argument, 'All comedians are funny people, some funny people are professors, therefore, some comedians are professors' is invalid because the overlap between comedians and professors--which would confirm the conclusion--is not mandatory from the premises.

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Most popular questions from this chapter

Use Euler diagrams to determine whether each argument is valid or invalid. All multiples of 6 are multiples of 3 . Eight is not a multiple of 3 . Therefore, 8 is not a multiple of 6 .

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.

In Exercises 1-24, use Euler diagrams to determine whether each argument is valid or invalid. All writers appreciate language. All poets are writers. Therefore, all poets appreciate language.

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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 all people obey the law, then no jails are needed. Some jails are needed. \(\therefore\) Some people do not obey the law.
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