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Chapter 3: Problem 50

Use the standard forms of valid arguments to draw a valid conclusion from the given premises. If I am a full-time student, I cannot work. If I cannot work, I cannot afford a rental apartment costing more than \(\$ 500\) per month. Therefore, ...

Short Answer

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If I am a full-time student, I cannot afford a rental apartment costing more than $500 per month.

Step by step solution

01

Identifying the Statements

The first step is to identify the individual conditional statements in the premises. The first statement is 'If I am a full-time student, then I cannot work.' The second statement is 'If I cannot work, then I cannot afford a rental apartment costing more than $500 per month.'
02

Applying Modus Ponens

Modus Ponens is a rule of inference which states that if we have a conditional statement of the form 'If P, then Q', and we know that 'P' is true, then we can conclude 'Q'. Here, the 'P' statement is 'I am a full-time student', and the 'Q' statement is 'I cannot work'. The next 'P' statement is 'I cannot work', and the 'Q' statement is 'I cannot afford a rental apartment costing more than $500 per month.' If we know that the first 'P' statement is true, namely that 'I am a full-time student', we can apply Modus Ponens twice to conclude the final 'Q' statement.
03

Formulating the Conclusion

Having applied Modus Ponens to our conditional statements, we can say that if 'I am a full-time student', then 'I cannot work' and thus 'I cannot afford a rental apartment costing more than $500 per month.'

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Most popular questions from this chapter

Describe what is meant by a valid argument.

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.

No animals that eat meat are vegetarians. No cat is a vegetarian. Felix is a cat. Therefore,,\(.\) a. Felix is a vegetarian. b. Felix is not a vegetarian. c. Felix eats meat. d. All animals that do not eat meat are vegetarians.

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 all people obey the law, then no jails are needed. Some jails are needed. \(\therefore\) Some people do not obey the law.

Use the standard forms of valid arguments to draw a valid conclusion from the given premises. The writers of My Mother the Car were told by the network to improve their scripts or be dropped from prime time. The writers of My Mother the Car did not improve their scripts. Therefore, ...
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