Some students were not involved in the strike.
If the above statement is true, which of the following conclusions is/are logically
necessary?
1. Some who were involved in the strike were students.
2. No student was involved in the strike.
3. At least one student was involved in the strike.
4. Some who were not involved in the strike were students.
Options:
(A) 1 and 2
(B) 3
(C) 4
(D) 2 and 3
Official Answer Key:
C
Step-by-Step Solution & Explanation
### **Official Solution & Concept Analysis (GATE BT 2019 Q.2)**
**1. Governing Concept**:
- **Topic**: Categorical Logic & Syllogisms (Square of Opposition)
- Given: The proposition *"Some students were not involved in the strike"* (Particular Negative, **O** proposition) is **FALSE**.
- By the Classical Square of Opposition:
- If **O** is False, its contradictory proposition **A** (*Universal Affirmative*: *"All students were involved in the strike"*) must be **TRUE**.
- If All students were involved, then naturally *"Some students were involved in the strike"* (**I** proposition, subaltern of A) is also true.
- Hence, *"All students were involved in the strike"* is definitely true.
**2. Option Analysis**:
- **Option (A) is INCORRECT**: Contradicts the falsity of O.
- **Option (B) is INCORRECT**: Cannot be determined if no students is claimed.
- **Option (C) [All students were involved in the strike] is CORRECT**: Direct contradictory of false proposition "Some students were not involved".
- **Option (D) is INCORRECT**: Fails logical square of opposition.
**3. Final Answer**:
- **Correct Choice**: **C**
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.