To find: Whether the stated conclusion is valid based on the given information, if not, write invalid.
Answer to Problem 4CYU
The conclusion is invalid.
Explanation of Solution
Given: If Elan stays up late, he will be tired the next day. Elan is tired.
Conclusion: Elan stayed up late.
Calculation:
First identify the hypothesis
Let
Let
Now analyze the conclusion.
The given statement “Elan is tired.” 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 “Elan stayed up late” is invalid.
Chapter 2 Solutions
Geometry, Student Edition
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