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.

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:

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).