In 2022, June Huh was awarded the Fields medal (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.
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Based only on the above information, which of the following statements can be logically inferred with certainty?
Show Hint
- Every Fields medalist has won a medal in an International Mathematics Olympiad.
- Everyone who has dropped out of college has won the Fields medal.
- All Fields medalists are part-time poets.
- Some Fields medalists have dropped out of college.
The Correct Option is D
Solution and Explanation
Step 1: Extract the given facts.
June Huh is a Fields medalist; he did not win any IMO medals; he dropped out of college; he was a poet when younger.
Step 2: Test each option against the facts.
(A) "Every Fields medalist has an IMO medal."
Counterexample: June Huh is a Fields medalist with no IMO medals \(\Rightarrow\) (A) is certainly false.
[2mm]
(B) "Everyone who dropped out of college has a Fields medal."
We only know one dropout (June Huh) who has a Fields medal; this does not justify a universal claim about all dropouts \(\Rightarrow\) not inferable.
[2mm]
(C) "All Fields medalists are part-time poets."
We know only that one Fields medalist (June) was a poet when younger (not even stated 'part-time'). A universal statement about all medalists is unjustified \(\Rightarrow\) not inferable.
[2mm]
(D) "Some Fields medalists have dropped out of college."
"Some" means "at least one." June Huh is a Fields medalist who dropped out \(\Rightarrow\) (D) is certainly true.
Final Answer:
\[
\boxed{\text{(D) Some Fields medalists have dropped out of college.}}
\]
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