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
- Consider the following two phonological rules:
Rule 1: Vowel Epenthesis of [ɪ] after sibilant-ending stems
Rule 2: Progressive Voicing Assimilation of the plural affix
Which ONE of the following rule ordering relations apply in the case of regular English pluralization as in ‘horse’ – ‘horses’? - 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. Consider a five-digit number PQRST that has distinct digits P, Q, R, S and T, and satisfies the following conditions:
$P < Q$
$S > P > T$
$R < T$
If integers 1 through 5 are used to construct such a number, the value of P is:Residency is a famous housing complex with many well-established individuals among its residents. A recent survey conducted among the residents of the complex revealed that all of those residents who are well established in their respective fields happen to be academicians. The survey also revealed that most of these academicians are authors of some best-selling books.
Based only on the information provided above, which one of the following statements can be logically inferred with certainty?- The police arrested four criminals – P, Q, R and S. The criminals knew each other. They made the following statements:
P says "Q committed the crime.”
Q says "S committed the crime. "
R says"I did not do it."
S says "What Q said about me is false."
Assume only one of the arrested four committed the crime and only one of the statements made above is true. Who committed the crime?
