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?
Options:
(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.
Official Answer Key:
D
Step-by-Step Solution & Explanation
### **Official Solution & Concept Analysis (GATE BT 2023 Q.4)**
**1. Governing Concept**:
- **Topic**: Verbal Reasoning & Deductive Logic
- Given premises:
1. June Huh won the Fields medal.
2. June Huh dropped out of college.
- Because June Huh is an element of the set of Fields medalists, and June Huh is also in the set of college dropouts:
$\text{Fields Medalists } \cap \text{ College Dropouts} \neq \emptyset$
Therefore, "Some Fields medalists have dropped out of college" must be true with certainty.
**2. Option Analysis**:
- **Option (A) is INCORRECT**: Universal generalization contradicted by June Huh not winning an IMO medal.
- **Option (B) is INCORRECT**: Invalid converse affirming the consequent.
- **Option (C) is INCORRECT**: Overgeneralized to all medalists.
- **Option (D) is CORRECT**: A direct, logically sound existential deduction from the single verified instance of June Huh.
**3. Final Answer**:
- **Correct Choice**: **D**
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