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Chapter 3: Problem 17

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.) There must be a dam or there is flooding. This year there is flooding. \(\therefore\) This year there is no dam.

Short Answer

Expert verified
The argument 'There must be a dam or there is flooding. This year there is flooding. Hence, this year there is no dam.' is invalid, as there can be a scenario where both flooding and the dam exist, contradicting the conclusion.

Step by step solution

01

Identify the statements

Let's use \(D\) to represent the statement 'There is a dam.' and \(F\) for 'There is flooding.' Thus, three parts of the argument are \('D \lor F'\) meaning 'There must be a dam or there is flooding.', \(F\) indicating 'This year there is flooding.' and \(\neg D\) meaning 'This year there is no dam.'
02

Translate into Symbolic Form

The argument can now be translated into symbolic form, \((D \lor F), F \therefore \neg D \) which can be read as 'If there is a dam or flooding, and there is flooding this year, then there is no dam this year.'
03

Evaluate Argument using Truth Table

A truth table, with two binary variables D and F with possible values of True (T) or False (F), can be used to evaluate the argument. Considering all possible combinations, there will be one case where the premises are true and the conclusion is false. This is where D is true and F is true. In this scenario, the claim that D or F is true which means the flooding occurs even when there is a dam. This makes the argument invalid.

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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 it rains or snows, then I read. I am reading. \(\therefore\) It is raining or snowing.

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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.
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