Syllogism – Resolve what must be true Statements: 1) Some pearls are stones. 2) Some stones are diamonds. 3) No diamond is a gem. Conclusions: I) Some gems are pearls. II) Some gems are diamonds. III) No gem is a diamond. IV) No gem is a pearl.
Verbal Reasoning
Logical Deduction
Difficulty: Easy
Choose an option
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AOnly I and II follow
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BOnly III and IV follow
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COnly either I or IV and either II or III follow
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DOnly III and either I or IV follow
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ENone of these
Answer
Correct Answer: None of these
Explanation
Introduction / Context:This question mixes particular statements with a universal negative. The goal is to identify the conclusion(s) that necessarily follow, not just those that could be true in some imagined case.
Given Data / Assumptions:
- P ∩ S ≠ ∅ (some pearls are stones)
- S ∩ D ≠ ∅ (some stones are diamonds)
- D ∩ G = ∅ (no diamond is a gem)
Concept / Approach:Universal negatives transfer across equivalence: 'No diamond is a gem' is the same as 'No gem is a diamond'. However, the premises do not relate pearls to gems at all, so any assertion about gems and pearls must be treated cautiously.
Step-by-Step Solution:
II: Some gems are diamonds. Directly contradicts D ∩ G = ∅; therefore II is false.III: No gem is a diamond. This is the contrapositive form of the given universal negative and does follow.I: Some gems are pearls. There is no link connecting pearls to gems, so I does not follow.IV: No gem is a pearl. Also not compelled by the premises; pearls unrelated to gems could or could not overlap.Verification / Alternative check:
Build two consistent models: (A) Some pearls are gems (still no diamond is a gem), or (B) No pearl is a gem. Both satisfy the premises, showing neither I nor IV is necessary. Only III is guaranteed.Why Other Options Are Wrong:
A and B: Include conclusions about gems–pearls that are not forced.C or D: Use either–or structures that presuppose necessity where there is none, and in C include II which is impossible.Common Pitfalls:
Treating unrelated sets as if they must overlap or be disjoint; overlooking that the only guaranteed universal here is about diamonds and gems.Final Answer:None of these