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Chapter 3: Problem 10

Write the negation of each conditional statement. \(\sim p \rightarrow r\)

Short Answer

Expert verified
The negation of the conditional statement \(\sim p \rightarrow r\) is \(\sim p \land \sim r\).

Step by step solution

01

Understand the Statement

Recognize that the given statement is a conditional statement and it is in the form \((p \rightarrow r)\). The symbol \('\rightarrow'\) means 'implies or if-then.' In the given statement, \('\sim p'\) means 'not p' and \('r'\) is just \('r'\).
02

Write the Negation

The negation of a conditional statement \((p \rightarrow r)\) is given by \((p \land \sim r)\). Here, the 'and' operator is represented by \('\land'\). So, the negation of the given statement, \(\sim p \rightarrow r\), is \((\sim p \land \sim r)\). The symbol \('\sim r'\) means 'not r'.

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Most popular questions from this chapter

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.

This is an excerpt from a 1967 speech in the U.S. House of Representatives by Representative Adam Clayton Powell: He who is without sin should cast the first stone. There is no one here who does not have a skeleton in his closet. I know, and I know them by name. Powell's argument can be expressed as follows: No sinner is one who should cast the first stone. All people here are sinners. Therefore, no person here is one who should cast the first stone. Use an Euler diagram to determine whether the argument is valid or invalid.

Use Euler diagrams to determine whether each argument is valid or invalid. All dancers are athletes. Savion Glover is a dancer. Therefore, Savion Glover is an athlete.

Use Euler diagrams to determine whether each argument is valid or invalid. All comedians are funny people. Some funny people are professors. Therefore, some comedians are professors.

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.) We criminalize drugs or we damage the future of young people. We will not damage the future of young people. \(\therefore\) We criminalize drugs.
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