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.

Difficulty: Medium

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.

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