Which of these is a valid conclusion?
Answer
A. All sergeants clear a fitness test.
Harry has cleared a fitness test.
Therefore, Harry is a sergeant.
B. All sergeants clear a fitness test.
Harry has not cleared a fitness test.
Therefore, Harry is not a sergeant.
C. All sergeants clear a fitness test.
Harry is a sergeant.
Therefore, Harry has not cleared a fitness test.
D. All sergeants clear a fitness test.
Harry is not a sergeant.
Therefore, Harry has not cleared a fitness test.
The valid conclusion is B. "All sergeants clear a fitness test. Harry has not cleared a fitness test. Therefore, Harry is not a sergeant."
To arrive at this conclusion, we need to consider the given statement that all sergeants clear a fitness test. This means that anyone who clears the fitness test is a sergeant, and anyone who does not clear the test is not a sergeant.
In option A, the conclusion states that Harry is a sergeant because he cleared the fitness test. However, this is not a valid conclusion as someone other than a sergeant could also clear the test.
In option C, the conclusion states that Harry has not cleared a fitness test because he is a sergeant. But it is not necessary that all sergeants have cleared the test, so this conclusion is also invalid.
In option D, the conclusion states that Harry has not cleared a fitness test because he is not a sergeant. This is not a valid conclusion, as there could be other reasons why Harry did not clear the test.
Therefore, the correct answer is option B, which concludes that Harry is not a sergeant because he has not cleared the fitness test, aligning with the given statement.