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
Verbal Reasoning
Logical Deduction
Difficulty: Medium
Choose an option
Answer
Correct Answer: Neither I nor II follows
Explanation
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 / logic1) 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 AnswerNeither I nor II follows.