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Chapter 3: Problem 30
Determine whether each argument is valid or invalid. All \(A\) are \(B\), no \(C\) are \(B\), and all \(D\) are \(C\). Thus, no \(A\) are \(D\).
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Use a truth table to determine whether the symbolic form of the argument is valid or invalid. $$ \begin{aligned} &(p \rightarrow q) \wedge(q \rightarrow p) \\ &\frac{p}{\therefore p \vee q} \end{aligned} $$
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.
Determine whether each statement makes sense or does not make sense, and explain your reasoning. I used Euler diagrams to determine that an argument is valid, but when I reverse one of the premises and the conclusion, this new argument is invalid.
Use Euler diagrams to determine whether each argument is valid or invalid. No blank disks contain data. Some blank disks are formatted. Therefore, some formatted disks do not contain data.
Explain how to use Euler diagrams to determine whether or not an argument is valid.
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