Which of the following statements are logically equivalent?

A. No philosophers are underpaid scholars.

B. All Philosophers are non-underpaid scholars.

C. No underpaid scholars are philosophers.

D. All non-underpaid scholars are non-philosophers.

Choose the correct answer from the options given below: 

The correct answer is A, B, and C Only
Important PointsThe correct answer is A, B, and C Only.

Statements A, B, and C are logically equivalent because they all express the same relationship between philosophers, underpaid scholars, and non-underpaid scholars. Let's examine each statement:

A. No philosophers are underpaid scholars:

• This statement asserts that there is no overlap between the category of philosophers and underpaid scholars.
• It implies that all philosophers are not underpaid scholars.

B. All Philosophers are non-underpaid scholars:

• This statement states that all philosophers fall within the category of non-underpaid scholars.
• It implies that there is no overlap between philosophers and underpaid scholars.

C. No underpaid scholars are philosophers:

• This statement states that there is no overlap between the category of underpaid scholars and philosophers.
• It implies that all underpaid scholars are not philosophers.

Additional Information

• These three statements convey the same logical relationship, expressing that philosophers and underpaid scholars do not overlap.
• However, statement D is not logically equivalent to the others because it makes a different assertion about non-underpaid scholars and non-philosophers, which is not directly related to the relationship between philosophers and underpaid scholars.