Errors in Reasoning Questions - - Question 10

To become an expert on a musical instrument, a person must practice. If people practice a musical instrument for thre...

AddisonPatton August 19, 2019

A vs C

I chose B as the correct answer but I am just curious to know if my thinking is correct. It sounds to me like answer choices A and C are saying the same thing in a way (that you absolutely have to practice for 3 hours every day in order to become an expert). Am I correct in thinking this or am I misunderstanding the answer choices?

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Irina August 28, 2019

@AddisonPatton,

Let's briefly look at the structure of the argument:

To become an expert, a person must practice.

Expert -> practice

If people practice for three hours a day, they will eventually become experts.

Practice 3x -> expert

Therefore, if a person is an expert, that person must have practiced for at least 3 hours a day.

Expert -> practice 3x.

This is flawed logic because it confuses a sufficient condition - practice 3 x - with a necessary condition - expert. We can conclude that if one practices 3x a day, this fact guarantees that one will become an expert. But we cannot conclude that if one is an expert, he must have practiced three hours a day because he could have practiced a different amount of time/ on a different schedule. Per our first premise, we see that for one to be an expert, one must practice but we cannot conclude that it must be 3x a day.

Your intuition with (A) and (C) is correct. (A) is incorrect because the argument's conclusion tells us that "if one is an expert..then..", hence, we only consider a scenario where one is an expert is true, so a scenario where one is not an expert is irrelevant. (C) describes the contrapositive of the conclusion - ~ practice 3 x-> ~ expert. Since this statement is logically equivalent to the conclusion, the conclusion does in fact take into account this possibility.

Let me know if you have any further questions.