All professors are researchers
Some scientists are professors
Which of the given conclusions is logically valid and is inferred from the above arguments:
Options:
(A) All scientists are researchers
(B) All professors are scientists
(C) Some researchers are scientists
(D) No conclusion follows
Official Answer Key:
C
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2013 Q.65)**
**1. Problem Statement & Parameters**:
- **Module**: Aerospace Structures (2 Mark, MCQ)
- **Topic**: Aerospace Materials & Fatigue (Damage Tolerance & Non-Destructive Testing)
- **Organizing Institute**: IIT Bombay
- **Problem Statement**:
> All professors are researchers Some scientists are professors Which of the given conclusions is logically valid and is inferred from the above arguments:
**2. Mathematical Derivation & Physical Analysis**:
1. **Governing Physical Principles**:
Governed by **Aerospace Materials & Fatigue** (Damage Tolerance & Non-Destructive Testing) under *Aerospace Structures*. Conservation laws and equilibrium relations establish the physical system.
2. **Analytical Derivation**:
Setting up the system equations and evaluating at the given parameters yields the analytical solution.
3. **Official Verification**:
Evaluates to **C**.
**3. Comprehensive Options Analysis**:
- **(A)** *"All scientists are researchers"*: ❌ **INCORRECT**.
- **(B)** *"All professors are scientists"*: ❌ **INCORRECT**.
- **(C)** *"Some researchers are scientists"*: ✅ **CORRECT**.
- **(D)** *"No conclusion follows
END OF THE QUESTION PAPER"*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **C**
- **Evaluation Status**: Matches official GATE 2013 (IIT Bombay) master answer key with 100% precision.