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Chapter 3: Problem 12

Determine whether or not each sentence is a statement. No U.S. president was an only child.

Short Answer

Expert verified
The sentence 'No U.S. president was an only child.' was determined to be a statement because it holds a definitive truth value which is false. Also, it is not both true and false at the same time, which satisfies the condition for a sentence to be a statement in logic.

Step by step solution

01

Understand the sentence

First, it is important to understand what the sentence is saying. The sentence 'No U.S. president was an only child.' is making a categorical claim about all U.S. presidents.
02

Determine if it is true or false

To determine if a sentence is a statement, it must be possible for it to be either true or false but not both. If every U.S. president was an only child, then the sentence would be false. Conversely, if at least one U.S. president was an only child, then the sentence is true.
03

Deliver the conclusion

Upon research, one can find that indeed, there have been U.S. Presidents that were only children. Thus, the proposition 'No U.S. president was an only child.' is indeed false. It's important to note that even though the proposition is false, it's still a statement because it is able to maintain a definitive truth value, which is false.

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Most popular questions from this chapter

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 we close the door, then there is less noise. There is less noise. \(\therefore\) We closed the door.

In this section, we used a variety of examples, including arguments from the Menendez trial, the inevitability of Nixon's impeachment, Spock's (fallacious) logic on Star Trek, and even two cartoons, to illustrate symbolic arguments. a. From any source that is of particular interest to you (these can be the words of someone you truly admire or a person who really gets under your skin), select a paragraph or two in which the writer argues a particular point. (An intriguing source is What Is Your Dangerous Idea?, edited by John Brockman, published by Harper Perennial, 2007.) Rewrite the reasoning in the form of an argument using words. Then translate the argument into symbolic form and use a truth table to determine if it is valid or invalid. b. Each group member should share the selected passage with other people in the group. Explain how it was expressed in argument form. Then tell why 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 I am at the beach, then I swim in the ocean. If I swim in the ocean, then I feel refreshed. \(\therefore\) If I am at the beach, then I feel refreshed.

Draw what you believe is a valid conclusion in the form of a disjunction for the following argument. Then verify that the argument is valid for your conclusion. "Inevitably, the use of the placebo involved built-in contradictions. A good patient-doctor relationship is essential to the process, but what happens to that relationship when one of the partners conceals important information from the other? If the doctor tells the truth, he destroys the base on which the placebo rests. If he doesn't tell the truth, he jeopardizes a relationship built on trust."

Use a truth table to determine whether the symbolic form of the argument is valid or invalid. $$ \begin{aligned} &p \rightarrow q \\ &\underline{q \rightarrow r} \\ &\therefore \sim p \rightarrow \sim r \end{aligned} $$
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