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Chapter 3: Problem 47

Use the standard forms of valid arguments to draw a valid conclusion from the given premises. If all electricity is off, then no lights work. Some lights work. Therefore, ...

Short Answer

Expert verified
Therefore, all electricity is not off.

Step by step solution

01

Analyze the Premises

The first premise says that 'If all electricity is off, then no lights work.' This is a conditional statement, or implication, of the form 'If P, then Q'. The second premise says 'Some lights work.' which is a positive (or affirmative) statement.
02

Identify the Type of Logical Argument Involved

The premises and the structure of the argument suggest that the form of logical argument at play is 'modus tollens'. Modus tollens has the form 'If P, then Q. Not Q. Therefore, Not P.' Here, 'P' corresponds to 'all electricity is off' and 'Q' corresponds to 'no lights work.' Therefore, given the positive statement, we can deduce 'Not Q.'
03

Draw a Valid Conclusion

Applying modus tollens, If we assume 'If P, then Q. Not Q.', it leads to the conclusion 'Therefore, Not P.' Here, 'Not P' corresponds to 'All electricity is not off.'

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Most popular questions from this chapter

Describe what is meant by a valid argument.

Translate each argument into symbolic form. Then determine whether the argument is valid or invalid. It is the case that \(x<5\) or \(x>8\), but \(x \geq 5\), so \(x>8\).

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.

Under what circumstances should Euler diagrams rather than truth tables be used to determine whether or not an argument is valid?

Use Euler diagrams to determine whether each argument is valid or invalid. All thefts are immoral acts. Some thefts are justifiable. Therefore, some immoral acts are justifiable.
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