Syllogism — Pens, pencils, and erasers (universal negative via subset): Statements: • All pens are pencils. • No pencil is an eraser. Conclusions: I. No eraser is a pen. II. No pen is an eraser.

Introduction / Context:
We combine a subset relation with a universal exclusion. The key is to see that exclusions apply to all subsets of the excluded class.

Given Data / Assumptions:

• Pen ⊆ Pencil.
• Pencil ∩ Eraser = ∅.

Concept / Approach:
If nothing in Pencil is an Eraser, then no Pen (being a Pencil) can be an Eraser. The converse statement “No eraser is a pen” also follows because if an Eraser were a Pen, it would be a Pencil, contradicting the exclusion.

Step-by-Step:
1) From Pen ⊆ Pencil and Pencil ∩ Eraser = ∅, infer Pen ∩ Eraser = ∅ → II follows.2) Suppose, for contradiction, an Eraser is a Pen. Then it is a Pencil, violating Pencil ∩ Eraser = ∅ → I follows.

Common Pitfalls:
Believing only one direction holds; here both non-membership statements are equivalent because of the subset.

Final Answer:
Both conclusions I and II follow.