7) If a number is divisible by 3, then the sum of the digits of that number is divisible by 3.
The sum of the digits of a number is not divisible by 3. Therefore the number is not divisible by 3.
A) affirming the hypothesis
B) denying the conclusion
C) both affirming the hypothesis and denying the conclusion
D) neither affirming the hypothesis nor denying the conclusion
The correct answer is B) denying the conclusion.
To determine the answer, let's break down the argument and examine its logical structure.
The argument starts with the hypothesis that if a number is divisible by 3, then the sum of the digits of that number is divisible by 3. This is a conditional statement, where the condition is "a number is divisible by 3" and the result is "the sum of the digits of that number is divisible by 3."
The argument then presents a specific case where the sum of the digits of a number is not divisible by 3. Based on this specific case, the argument concludes that the number is not divisible by 3.
Now, let's apply some critical thinking to the argument. The argument starts with a general rule stating that if a number is divisible by 3, then the sum of the digits is divisible by 3. The specific case presented in the argument goes against this general rule. However, a single specific case does not invalidate a general rule.
In this case, the argument denies the conclusion based on a single counterexample. This means that the general rule might still be true, but there is at least one exception. To affirm the hypothesis, we would need to show that every number that is divisible by 3 has a sum of digits divisible by 3. To deny the conclusion, we only need to provide one counterexample where the sum of digits is not divisible by 3. Therefore, the argument denies the conclusion by presenting a counterexample.
Hence, the correct answer is B) denying the conclusion.