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Chapter 3: Problem 33

Determine whether each argument is valid or invalid. No \(A\) are \(B\), no \(B\) are \(C\), and no \(C\) are \(D\). Thus, no \(A\) are \(D\).

Short Answer

Expert verified
The argument 'No A are B, No B are C, and No C are D, thus no A are D' is valid.

Step by step solution

01

Explain the Premises

First, understand each of the premises. 'No A are B' implies that there is no overlap between the sets A and B. Similarly, 'No B are C' and 'No C are D' imply that there is no overlap between the sets B and C, and the sets C and D, respectively.
02

Establish Logical Connections

Next, find the logical connection between the statements. The logical progression goes from A to B, from B to C, and then from C to D. Since A doesn't overlap with B, then B doesn't overlap with C, and C doesn't overlap with D, it can be deduced, by transitivity, that A doesn't overlap with D.
03

Conclusion Evaluation

Finally, evaluate the given conclusion 'No A are D'. Because of the previously established logical connections, it's clear that if A can't overlap with B and B can't overlap with C and C can't overlap with D, then A can't overlap with D. Thus, the final statement 'No A are D' is a valid conclusion, drawn from the given premises.

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Most popular questions from this chapter

If you are given an argument in words that contains two premises and a conclusion, describe how to determine if the argument is valid or invalid.

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.

Use the standard forms of valid arguments to draw a valid conclusion from the given premises. If I vacation in Paris, I eat French pastries. If I eat French pastries, I gain weight. Therefore, ...

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.

Under what circumstances should Euler diagrams rather than truth tables be used to determine whether or not an argument is valid?
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