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
- The following observation is made about the scores obtained by 100 students in an exam:
'For each student, there exists another student in the class such that their scores are at most ten marks away.'
If the above statement is false, which one of the following statements is necessarily true? - 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’? Consider a linear arrangement of seven bulbs, each of which can be in the ON or OFF states. The initial configuration of the bulbs is shown in the figure. In every Step, the states of the bulbs are changed based on the following rules:
- Any OFF bulb with exactly one ON neighbor at the end of the previous Step is turned ON.
- Any ON bulb with both neighbors ON at the end of the previous Step is turned OFF.
- The state of any bulb not meeting the conditions above is left unchanged.
The state of bulbs at the end of Step 1 and Step 2 are also shown in the figure.
The number of bulbs which are ON at the end of Step 8 is ______
- 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:
