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.
Analyzing Logical Conclusions from a Statement
The problem requires identifying which conclusions logically and necessarily follow from the premise: "Some students were not involved in the strike". We will analyze each conclusion based on this premise.
Premise Analysis
The core premise is "Some students were not involved in the strike." This means that there is at least one individual who fits both criteria: being a student and not being involved in the strike.
Conclusion Verification
- Conclusion 1: Some who were involved in the strike were students.
The premise only provides information about students who were *not* involved. It does not give any information about students who *were* involved or non-students who were involved. Therefore, this conclusion is not necessarily true.
- Conclusion 2: No student was involved in the strike.
This statement claims that *all* students were uninvolved. The premise, however, only states that *some* students were uninvolved. It's possible that other students *were* involved. This conclusion is not necessarily true and could even be false.
- Conclusion 3: At least one student was involved in the strike.
Similar to conclusion 2, the premise guarantees only that some students were *not* involved. It is logically possible that *all* students were not involved in the strike. If all students were not involved, the premise "Some students were not involved" would still be true. Thus, this conclusion is not necessarily true.
- Conclusion 4: Some who were not involved in the strike were students.
This statement asserts that there exists at least one person who was not involved in the strike and who is also a student. This is exactly what the premise "Some students were not involved in the strike" means. Therefore, this conclusion is logically necessary.
Final Determination
Based on the logical analysis, only Conclusion 4 is a necessary consequence of the given premise.
Important Questions from Logical Deduction
- Based only on the conversation below, identify the logically correct inference:
“Even if I had known that you were in the hospital, I would not have gone there to see you", Ramya told Josephine. In the given figure, the numbers associated with the rectangle, triangle, and ellipse are 1, 2, and 3, respectively. Which one among the given options is the most appropriate combination of P, Q, and R ?
- Column-I has statements made by Shanthala; and, Column-II has responses given by Kanishk.
Column-I Column-II P. This house is in a mess. 1. Alright, I won't bring it up during our conversations. Q. I am not happy with the marks given to me. 2. Well, you can easily look it up. R. Politics is a subject I avoid talking about. 3. No problem, let me clear it up for you. S. I don't know what this word means. 4. Don't worry, I will take it up with your teacher.
Identify the option that has the correct match between Column-I and Column-II. - In the following truth table, what does X stand for?
P Q X 1 1 1 1 0 0 0 1 0 0 0 1 A color model is shown in the figure with color codes: Yellow (Y), Magenta (M), Cyan (Cy), Red (R), Blue (Bl), Green (G), and Black (K).
Which one of the following options displays the color codes that are consistent with the color model?
