An object is said to have an n-fold rotational symmetry if rotation by an angle of 360°/n leaves the object invariant. For an equilateral triangle in a plane, the order of rotational symmetry n is:
Options:
(A) 3 (rotation by 120°)
(B) 2 (rotation by 180°)
(C) 4 (rotation by 90°)
(D) 6 (rotation by 60°)
Official Answer Key:
A
Step-by-Step Solution & Explanation
### **Official Solution & Concept Analysis (GATE BT 2025 Q.10)**
**1. Governing Concept**:
- **Topic**: Verbal Reasoning & Logical Deductions (Syllogisms)
- Deductive inference from categorical premises using Venn set diagrams.
**2. Option Analysis**:
- Tracing valid existential and universal quantifiers confirms Option (C) as the only logically necessary deduction.
- **Option (C) is CORRECT**.
- **Options (A), (B), and (D) are INCORRECT**: Commit logical fallacies (illicit conversion or undistributed middle).
**3. Final Answer**:
- **Correct Choice**: **C**
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