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Chapter 3: Problem 6
Write the negation of each conditional statement. If she says yes, he says no.
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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 am tired or hungry, I cannot concentrate. I cannot concentrate. \(\therefore\) I am tired or hungry.
Determine whether each statement makes sense or does not make sense, and explain your reasoning. I can't use Euler diagrams to determine the validity of an argument if one of the premises is false.
Use a truth table to determine whether the symbolic form of the argument is valid or invalid. $$ \begin{aligned} &(p \rightarrow q) \wedge(q \rightarrow p) \\ &\frac{p}{\therefore p \vee q} \end{aligned} $$
Use a truth table to determine whether the symbolic form of the argument is valid or invalid. $$ \begin{aligned} &p \rightarrow q \\ &\underline{q \rightarrow r} \\ &\therefore \sim p \rightarrow \sim r \end{aligned} $$
Describe what is meant by a valid argument.
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