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Chapter 3: Problem 118

Determine whether each statement makes sense or does not make sense, and explain your reasoning. Earth is the only planet not named after a god, so not being named after a god is both necessary and sufficient for a planet being Earth.

Short Answer

Expert verified
The statement makes sense. Not being named after a god would be both a necessary and sufficient condition for a planet to be Earth.

Step by step solution

01

Analyze the statement

The first step is to carefully analyze the statement. The proposition 'Earth is the only planet not named after a god, so not being named after a god is both necessary and sufficient for a planet being Earth.' is given. Review the implications of the necessary and sufficient conditions.
02

Interpret necessary condition

Necessary means that if the second condition is true (a planet is not named after a god), then the first condition has to be true (it must be Earth). This interpretation would imply that only Earth is not named after a god and thus, every planet not named after a god must be Earth.
03

Interpret sufficient condition

Sufficient means that if the first condition is true (a planet is Earth), then the second condition has to be true (it is not named after a god). This interpretation would imply that every time we are dealing with Earth, it is guaranteed to be a planet not named after a god.
04

Evaluate statement

Given both conditions and interpretations, the statement makes sense because Earth is indeed the only planet not named after a god. Therefore, not being named after a god is indeed both necessary and sufficient for a planet to be Earth.

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Most popular questions from this chapter

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 we close the door, then there is less noise. There is less noise. \(\therefore\) We closed the door.

Conservative commentator Rush Limbaugh directed this passage at liberals and the way they think about crime. Of course, liberals will argue that these actions [contemporary youth crime] can be laid at the foot of socioeconomic inequities, or poverty. However, the Great Depression caused a level of poverty unknown to exist in America today, and yet I have been unable to find any accounts of crime waves sweeping our large cities. Let the liberals chew on that. (See, I Told You So, p. 83) Limbaugh's passage can be expressed in the form of an argument: If poverty causes crime, then crime waves would have swept American cities during the Great Depression. Crime waves did not sweep American cities during the Great Depression. \(\therefore\) Poverty does not cause crime. (Liberals are wrong.) Translate this argument into symbolic form and determine whether it is valid or invalid.

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

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.

Write an original argument in words for the direct reasoning form.
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