Concept explainers
To find: Whether the stated conclusion is valid based on the given information, if not, write invalid.
Answer to Problem 20PPS
The conclusion is invalid.
Explanation of Solution
Given:
If Dante obtains a part-time job, he can afford a car payment. Dante can afford a car payment.
Conclusion: Dante obtained a part-time job.
Calculation:
First identify the hypothesis
Let
Let
Now analyze the conclusion.
The given statement “Dante can afford a car payment” satisfies the conclusion, so
Use the Law of Detachment,
“if
Therefore, by the Law of Detachment does not apply. It is known that a conditional statement and its conclusion are true does not make the hypothesis true. So, the conclusion “Dante obtained a part-time job” is invalid.
Chapter 2 Solutions
Geometry, Student Edition
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