Question

In 2022, June Huh was awarded the Fields medal, which is the highest prize in Mathematics.
When he was younger, he was also a poet. He did not win any medals in the International Mathematics Olympiads. He dropped out of college.
Based only on the above information, which one of the following statements can be logically inferred with certainty?

• A. Every Fields medalist has won a medal in an International Mathematics Olympiad.
• B. Everyone who has dropped out of college has won the Fields medal.
• C. All Fields medalists are part-time poets.
• D. Some Fields medalists have dropped out of college.

Hint:

Logical inferences can only be made based on the explicitly provided information. We cannot assume additional information or characteristics unless they are explicitly stated.

Answer 1

The Correct Option is B

The given information tells us that June Huh won the Fields medal and dropped out of college, but it does not specify whether every Fields medalist has dropped out of college or whether all Fields medalists share similar characteristics like winning medals in the International Mathematics Olympiad or being poets.
(A) is false because it is not stated that every Fields medalist wins an International Mathematics Olympiad medal.
(B) is false because the statement that "everyone who has dropped out of college has won the Fields medal" cannot be logically inferred from the provided information.
(C) is false because we are not told that all Fields medalists are poets.
(D) is true because it is logically inferred that June Huh, a Fields medalist, dropped out of college, implying that some Fields medalists have dropped out of college.
Thus, the correct answer is (B) and (D).