Syllogism — Premises: (a) All dogs are books. (b) All books are pictures. Conclusions: I) All dogs are pictures. II) All books are dogs. III) All pictures are dogs. IV) Some pictures are books.
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AOnly I and IV follow
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BOnly II and III follow
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CEither II or III follows
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DEither II or IV follows
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ENone of these
Answer
Correct Answer: Only I and IV follow
Explanation
Introduction / Context:Two nested universals are provided. We assess which of the four conclusions are compelled by these inclusions.
Given Data / Assumptions:
- Dogs ⊆ Books.
- Books ⊆ Pictures.
- Ordinary-language assumption: the class 'Books' is non-empty, so existential statements about some members are acceptable in exam settings.
Concept / Approach:Transitivity of subset gives Dogs ⊆ Pictures (I). The converses (II, III) are not supported. From Books ⊆ Pictures and non-emptiness, there exists at least one entity that is both picture and book, validating IV.
Step-by-Step Solution:
I) Dogs ⊆ Books and Books ⊆ Pictures imply Dogs ⊆ Pictures — true.II) 'All books are dogs': converse, not implied.III) 'All pictures are dogs': overly strong; not implied.IV) 'Some pictures are books': if any book exists, that book is a picture — validates an existential.Verification / Alternative check:Take one concrete book; it is also a picture, satisfying IV. Dogs being a subset of books ensures I.
Why Other Options Are Wrong:Options that include II or III assume unsupported converses or overgeneralization.
Common Pitfalls:Confusing subset direction and presuming equivalences where only one-way inclusion exists.
Final Answer:Only I and IV follow.