Syllogism – Three-term chain with one universal: Statements: Some tablets are capsules. All capsules are syrups. Some syrups are medicines. Conclusions: I) Some syrups are powders. II) Some syrups are tablets. Select the option that states what necessarily follows.

Difficulty: Easy

Correct Answer: Only Conclusion II follows

Explanation:


Introduction / Context:
This question tests core syllogism skills with set relations expressed via quantifiers 'some' and 'all'. The key terms are Tablets (T), Capsules (C), Syrups (S), Medicines (M), and Powders (P). We must decide which conclusions are true in every possible model that satisfies the given premises, not merely in a convenient example.



Given Data / Assumptions:

  • Premise 1: Some T are C (there exists at least one element that is both a Tablet and a Capsule).
  • Premise 2: All C are S (C ⊆ S).
  • Premise 3: Some S are M (there exists at least one Syrup that is a Medicine).
  • No information is provided about Powders (P), and we assume nothing beyond the premises.


Concept / Approach:
Use standard set/venn reasoning. A universal premise allows us to forward-chain membership from the subset to the superset. A particular ('some') establishes existence of at least one specific witness. Conclusions must hold for every model that satisfies the premises; otherwise they do not necessarily follow.



Step-by-Step Solution:
From Premise 1, pick an element x such that x ∈ T ∩ C.Premise 2 says C ⊆ S, so the same x is in S. Therefore x ∈ T ∩ S. Hence there exists a Syrup that is also a Tablet. This proves Conclusion II.Premise 3, 'Some S are M', is unrelated to Powders (P) and does not force any link between S and P. No premise states that any S is a Powder, so Conclusion I is not compelled.



Verification / Alternative check:
Construct a countermodel for Conclusion I: Let S contain two disjoint parts—one overlapping C (and therefore T) and another overlapping M; let P be disjoint from S. The premises remain true, yet no Syrup is a Powder. Therefore I does not necessarily follow. Conclusion II continues to hold because the specific tablet-capsule witness is also a Syrup by Premise 2.



Why Other Options Are Wrong:

  • Only Conclusion I follows: false; I has a clear countermodel.
  • Both follow / Either I or II follows: too strong; only II is guaranteed.
  • Neither follows: ignores the forced existence of a Syrup that is a Tablet.


Common Pitfalls:
Assuming that 'Some S are M' implies extra overlap with unrelated categories like Powders. Particular statements create existence but not universal spreading across unrelated sets.



Final Answer:
Only Conclusion II follows.

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