Q.2 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.
(A) 1 and 2 (B) 3 (C) 4 (D) 2 and 3

Logical Analysis of the Statement

The given statement is: “Some students were not involved in the strike.”

This is a categorical statement in logic, equivalent to “Some S are not P,” where S = students and P = those involved in the strike. It asserts that at least one student exists who was not involved, but says nothing definitive about students who were involved. We must evaluate which conclusions logically follow (i.e., are necessarily true if the statement is true).

Evaluation of Each Option

1. Some who were involved in the strike were students.
   This claims some P are S. The original statement doesn’t require any students to be involved—it only guarantees some were not involved. It’s possible all students were not involved. Thus, this is not necessarily true (possible but not required).

2. No student was involved in the strike.
   This claims no S are P (all students were not involved). However, the original allows for some students to be involved alongside those who weren’t. It’s possible some were involved. Thus, this is not necessarily true.

3. At least one student was involved in the strike.
   Similar to option 1, this requires at least one S is P. The original only guarantees some S are not P, so it’s possible zero students were involved. Thus, not necessarily true.

4. Some who were not involved in the strike were students.
   This claims some non-P are S, which is exactly the same as the original statement (“Some S are not P”). In categorical logic, this is the converse but equivalent in meaning for particular affirmatives/negatives here. It logically follows as necessarily true.

Correct Answer

Only option 4 is logically necessary. The answer is (C) 4.

Visual Representation (Venn Diagram Insight):
Imagine two overlapping circles: Students (S) and Involved in strike (P). The statement places at least one dot in S outside P. This doesn’t force dots in the S-P overlap, ruling out 1 and 3. Option 4 restates the dot’s position.

This article breaks down the key phrase “some students were not involved in the strike” for students tackling logical reasoning in competitive exams like IIT JAM. If you’re searching for “some students were not involved in the strike logic question”, you’ve found the expert solution with step-by-step analysis.

Understanding the Statement: Categorical Logic Basics

In logical reasoning, statements like “some students were not involved in the strike” follow Aristotelian syllogisms. Here:

• Students = S

• Involved in the strike = P

The statement translates to “Some S are not P” (particular negative). It guarantees existence: at least one student outside the “involved” group. No info on overlap.

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Option-by-Option Breakdown

Let’s evaluate each logical conclusion:

• Option 1: Some who were involved in the strike were students
  Claims “Some P are S.” Possible? Yes. Necessary? No—all students could avoid the strike. ❌

• Option 2: No student was involved in the strike
  Claims “No S are P.” Contradicts possibility of involvement. The statement allows partial involvement. ❌

• Option 3: At least one student was involved in the strike
  Requires “Some S are P.” No guarantee—could be zero involved. ❌

• Option 4: Some who were not involved in the strike were students
  Restates “Some non-P are S”—identical to original. Logically necessary. ✅

Answer Key: (C) 4. Perfect for IIT JAM logical reasoning practice.

Why This Matters for Competitive Exams

Questions like “some students were not involved in the strike” test logical necessity vs. possibility. Common trap: Confusing “some not” with “none” or “some yes.” Practice with 20+ similar PYQs.

Pro Tip: Use truth tables or Venns:

Only the “not P” part is forced.

Quick Practice Questions

1. If “All A are B,” what follows from “Some B are not A”? (Answer: Nothing necessary.)

2. Rephrase: “Some students were not involved in the strike” = Some non-strikers are students? (Yes!)

Master strike logic conclusions for IIT JAM success. Bookmark for logical reasoning tricks!

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