Syllogism — Pencils, Birds, Skies, Hills Statements: • All pencils are birds. • All birds are skies. • All skies are hills. Conclusions: I. All pencils are hills. II. All hills are birds. III. All skies are pencils. IV. All birds are hills.

Question

Solve this multiple-choice question and choose the correct option.

Accepted Answer

Introduction / Context:This is a straightforward chain of universal inclusions. Be careful not to reverse subset directions. From A ⊆ B ⊆ C ⊆ D, you can derive A ⊆ D and B ⊆ D, but not D ⊆ B or C ⊆ A. Given Data / Assumptions: Pencils ⊆ Birds ⊆ Skies ⊆ Hills. Concept / Approach:Transitivity of “All”: If X ⊆ Y and Y ⊆ Z, then X ⊆ Z. Do not invert inclusions unless explicitly given. Step-by-Step Solution: I. All pencils are hills — follows, since Pencils ⊆ Hills via the chain.II. All hills are birds — does not follow; the chain only shows Birds ⊆ Hills, not the converse.III. All skies are pencils — does not follow; Pencils ⊆ Birds ⊆ Skies, not Skies ⊆ Pencils.IV. All birds are hills — follows, because Birds ⊆ Skies ⊆ Hills. Verification / Alternative check:Draw nested sets: P ⊆ B ⊆ S ⊆ H. It is visually clear that I and IV are true while II and III are false. Why Other Options Are Wrong: Options a–c do not match the true pair {I, IV}. “All follow” is incorrect because II and III are false. Common Pitfalls:Accidentally reversing subset relations (assuming hills are birds, or skies are pencils). Final Answer:None of these (because the correct set is I and IV, a combination not listed).

Syllogism — Pencils, Birds, Skies, Hills Statements: • All pencils are birds. • All birds are skies. • All skies are hills. Conclusions: I. All pencils are hills. II. All hills are birds. III. All skies are pencils. IV. All birds are hills.

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