Syllogism — Premises: (a) All books are boxes. (b) All boxes are pens. (c) All pens are papers. Conclusions: I) Some papers are books. II) All books are papers. III) Some pens are books. IV) All boxes are books.
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AOnly conclusions I and III follow
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BEither conclusion II or IV follows
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COnly conclusions I, II and III follow
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DEither conclusion I or II or III follows
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ENone of these
Answer
Correct Answer: Only conclusions I, II and III follow
Explanation
Introduction / Context:We have a chain of three universal inclusions. We must test a mix of universal and existential conclusions.
Given Data / Assumptions:
- Books ⊆ Boxes.
- Boxes ⊆ Pens.
- Pens ⊆ Papers.
- Non-emptiness of Books for existential claims common in such tests.
Concept / Approach:By transitivity, Books ⊆ Papers (II). Therefore, if any book exists, it is a paper, validating I. Also, Books ⊆ Pens, so some pens are books (III) under non-emptiness. IV (All boxes are books) reverses inclusion and is invalid.
Step-by-Step Solution:
Step 1: Compose subsets: Books ⊆ Boxes ⊆ Pens ⊆ Papers.Step 2: Conclude II: All books are papers — true.Step 3: Existentials: pick any book b; since b ∈ Papers, I is true. Also b ∈ Pens, so III is true.Step 4: IV asserts Boxes ⊆ Books, which is converse and not supported.Verification / Alternative check:A concrete chain example quickly confirms I, II, III while falsifying IV by allowing boxes that are not books.
Why Other Options Are Wrong:Any option denying any of I–III or asserting IV conflicts with the chain.
Common Pitfalls:Overlooking that existential conclusions require at least one member, typically assumed in exam problems.
Final Answer:Only conclusions I, II and III follow.