Statements: • Some scales are pencils. • Some erasers are pencils. Conclusions: I. Some pencils are erasers. II. Some pencils are scales. Select the correct option.

Introduction / Context:
Here, each premise is an existential statement about overlap with the class “pencils.” We must decide whether each claimed overlap is guaranteed.

Given Data / Assumptions:

• Some Scales are Pencils ⇒ ∃x: x ∈ Scales ∩ Pencils.
• Some Erasers are Pencils ⇒ ∃y: y ∈ Erasers ∩ Pencils.

Concept / Approach:
When a premise says “Some X are P,” it already asserts the existence of pencils that are X. Therefore, each conclusion that restates the existence of pencils overlapping with the named set is immediately validated.

Step-by-Step Solution:
1) From Premise 2, there exists at least one pencil that is an eraser ⇒ Conclusion I is true.2) From Premise 1, there exists at least one pencil that is a scale ⇒ Conclusion II is true.3) No contradiction arises by having both exist simultaneously; they could be distinct or the same object, but existence is sufficient.

Verification / Alternative check:
Model: Let Pencils = {p1, p2}, Scales = {p1}, Erasers = {p2}. Both premises hold; both conclusions are satisfied.

Why Other Options Are Wrong:
Options “Only I” and “Only II” incorrectly deny one guaranteed existential. “Neither” and “Data inadequate” ignore that each premise already provides the needed existence.

Common Pitfalls:
Thinking that to assert “Some pencils are erasers” we must compare Scales and Erasers with each other. We do not: each premise independently witnesses an element of Pencils.

Final Answer:
Both I and II follow.