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Chapter 3: Problem 46
Write an example of an argument with two quantified premises that is invalid but that has a true conclusion.
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Determine whether each argument is valid or invalid. All \(A\) are \(B\), all \(B\) are \(C\), and all \(C\) are \(D\). Thus, all \(A\) are \(D\).
Use a truth table to determine whether the symbolic form of the argument is valid or invalid. $$ \begin{aligned} &p \leftrightarrow q \\ &\underline{q \rightarrow r} \\ &\therefore \sim r \rightarrow \sim p \end{aligned} $$
Use a truth table to determine whether the symbolic form of the argument is valid or invalid. $$ \begin{aligned} &p \rightarrow q \\ &\underline{q \rightarrow r} \\ &\therefore r \rightarrow p \end{aligned} $$
Use a truth table to determine whether the symbolic form of the argument is valid or invalid. $$ \begin{aligned} &\sim p \wedge q \\ &\frac{p \leftrightarrow r}{\therefore p \wedge r} \end{aligned} $$
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.
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