Syllogism with an individual instance: 'Some papers are pens' and 'Angle is a paper' — determine whether it necessarily follows that Angle is (or is not) a pen

Given data

• Premise 1: Some Papers are Pens (non-empty overlap).
• Premise 2: Angle is a Paper.
• Conclusions:
  • I: Angle is not a Pen.
  • II: Angle is a Pen.

Concept/Approach (why this method)

Knowing only that 'some papers are pens' does not tell us whether a particular paper (Angle) lies inside the overlapping region or outside it.

Step-by-Step calculation / logic
1) Model A: Angle lies in the intersection (Paper ∩ Pen) ⇒ II true, I false.2) Model B: Angle lies in the Paper-only region ⇒ I true, II false.3) Since truth varies by model consistent with premises, neither conclusion is necessary.

Verification/Alternative

Venn diagram quickly shows both placements for Angle are possible without violating premises.

Common pitfalls

• Marking 'Either I or II' on the basis of the law of excluded middle; syllogism validity demands necessity from premises, not mere tautology.

Final Answer
Neither I nor II follows.