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Chapter 3: Problem 92
Explain when biconditional statements are true and when they are false.
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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'm tired, I'm edgy. If I'm edgy, I'm nasty. \(\therefore\) If I'm tired, I'm nasty.
Use a truth table to determine whether the symbolic form of the argument is valid or invalid. $$ \begin{aligned} &p \leftrightarrow q \\ &\underline{q \rightarrow r} \\ &\therefore \sim r \rightarrow \sim p \end{aligned} $$
Translate the argument below into symbolic form. Then use a truth table to determine if the argument is valid or invalid. It's wrong to smoke in public if secondary cigarette smoke is a health threat. If secondary cigarette smoke were not a health threat, the American Lung Association would not say that it is. The American Lung Association says that secondary cigarette smoke is a health threat. Therefore, it's wrong to smoke in public.
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.
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 you tell me what I already understand, you do not enlarge my understanding. If you tell me something that I do not understand, then your remarks are unintelligible to me. \(\therefore\) Whatever you tell me does not enlarge my understanding or is unintelligible to me.
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