Question

Which of the following three inferences are valid? (There is no need to explain your answers.)

(a)        Premise:          Liu Yang spends two hours every day playing the violin.

Conclusion:      Liu Yang wants to be a good violinist.

(b)        Premise:          If Liu Yang is in class, she is on campus.

Premise:          Liu Yang is on campus.

Conclusion:      Liu Yang is in class.

(c)        Premise:          If Liu Yang is in class, she is on campus.

Premise:          Liu Yang is in class.

Conclusion:      Liu Yang is on campus.

Answer 1

Since you have said there is no need for an explanation, let me state right here that the only correct inference is in option C.

In case an explanation is required, refer to the following paragraphs.

a) Option A says that Liu Yang spends 2 hours every day playing the violin. This is the premise. However this premise mentions no fact that says that she wants to be a good violinist. An inference can only be drawn if some axioms of logic are satisfied. here we cannot see the satisfaction of any exams since the statement given as the conclusion does not exist anywhere else in the premise and is also not the universal fact.

Applying common sense we can find numerous reasons why Liu Yang please please the violin for 2 hours, for example it might be required by her curriculum, or it could be a case of pressure.

so just because she please the violin for 2 hours does it mean we can conclude that she wants to be a good violinist.

Hence inference in option A is invalid.

b) Option B has the first premise that "If Liu Yang is in class, she is on campus". The second premise is that "Liu Yang is on campus". Now modus ponens states that if a is true, and a implies b, is true then b is also true. However if we consider a as "Liu Yang is in class", and b as "Liu Yang is on campus", we know that a implies B, and b is a premise, therefore b is true. Clearly modus ponens cannot be applied to this situation. We also cannot find any other excuse that can make a true.

Hence, inference B is invalid.

c) Here, the first premise is "If Liu Yang is in class, she is on campus". Let b="Liu Yang is on campus". The second premise is "Liu Yang is in class"=a(say). So, according to the first premise, a implies b. According to the second premise a is true. So using modus ponens we can say that b is true, i.e., Liu Yang is on campus. Show the conclusion mentioned in option c is correct.

Hence, the inference in option C is valid.