Difficulty: Medium
Correct Answer: Set I and Set II
Explanation:
Introduction / Context:
This question tests your understanding of categorical logic involving institutes called IIMs and BIMs. Each numbered set (I–IV) contains three statements. In each set, you must determine whether the third statement is a conclusion that necessarily follows from the first two when combined, and that it cannot be deduced from either of them alone.
Given Data / Assumptions:
Concept / Approach:
For each set, we must check:
1) Whether the third statement follows logically from the first two taken together.
2) Whether it cannot be derived from either of the first two individually.
If both conditions are satisfied, that set qualifies. We then select the option that lists all and only such qualifying sets.
Step-by-Step Solution:
Step 1: Analyse Set I.
Premise 1: All IIMs are in India.
Premise 2: No BIMs are in India (i.e., BIMs are outside India).
Conclusion: No IIMs are BIMs.
From Premise 1, every IIM lies inside India. From Premise 2, no BIM is in India at all. Thus, no institute can be both an IIM and a BIM; otherwise it would have to be both in India and not in India at the same time. So the third statement follows from the combination of the first two.
Step 2: Check independence for Set I.
From Premise 1 alone, we only know that IIMs are in India; nothing about BIMs.
From Premise 2 alone, we only know that BIMs are not in India; nothing about IIMs.
Neither premise alone implies “No IIMs are BIMs”. It is the combination that yields this conclusion. So Set I qualifies.
Step 3: Analyse Set II.
Premise 1: All IIMs are in India.
Premise 2: No BIMs are in India.
Conclusion: No BIMs are IIMs.
This conclusion is just another way of saying “there is no institute that is both BIM and IIM”. The reasoning is the same as in Set I: IIMs are all inside India, BIMs are all outside India, so they cannot overlap. The third statement follows from the combination of the first two but not from either alone. Therefore, Set II also qualifies.
Step 4: Analyse Sets III and IV.
In both sets, the premises say that some IIMs and some BIMs are outside India. However, that does not logically force any overlap between IIMs and BIMs; they could be in completely different non-Indian countries. Therefore, conclusions like “Some IIMs are BIMs” or “Some BIMs are IIMs” do not follow necessarily from the premises, so Sets III and IV do not qualify.
Verification / Alternative check:
To see why Sets III and IV fail, consider an example where some IIMs are in country X (outside India) and some BIMs are in country Y (also outside India). Both premises in Set III or Set IV can be satisfied without any institute being both an IIM and a BIM. This shows that the third statements in III and IV are not logically forced by their premises.
Why Other Options Are Wrong:
Option A (“Set I only”) is wrong because Set II also satisfies the requirement for a valid conclusion derived from both premises.
Option B (“Set II only”) is wrong for the same reason; it excludes Set I, which is valid.
Option D (“Set III and Set IV”) is wrong because the third statements in III and IV do not necessarily follow from their premises; they are merely possible, not guaranteed.
Common Pitfalls:
Many students focus only on whether the conclusion sounds plausible rather than whether it is logically necessary. Another error is to overlook the requirement that the conclusion must not be derivable from a single premise alone. For sets I and II, the disjointness between IIMs and BIMs genuinely requires using both premises together.
Final Answer:
Therefore, the sets where the third statement is a necessary conclusion from both of the first two statements, and not from either alone, are Set I and Set II.
Discussion & Comments