To find: Whether the stated conclusion is valid based on the given information, if not, write invalid.
Answer to Problem 19PPS
The conclusion is invalid.
Explanation of Solution
Given:
If you leave your lights on while your car is off, your battery will die. Your battery is dead.
Conclusion: You left your lights on while the car was off.
Calculation:
First identify the hypothesis
Let
Let
Now analyze the conclusion.
The given statement “Your battery is dead” 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 “You left your lights on while the car was off” is invalid.
Chapter 2 Solutions
Geometry, Student Edition
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