Syllogism — Premises: (a) All pens are papers. (b) No eraser is a paper. Conclusions: I) No eraser is a pen. II) Some papers are pens.

Difficulty: Easy

Correct Answer: Both Conclusions I and II follow.

Explanation:


Introduction / Context:
We combine a universal inclusion with a universal exclusion and test both a universal negative and an existential conclusion.


Given Data / Assumptions:

  • Pens ⊆ Papers.
  • Erasers ∩ Papers = ∅.
  • Assume at least one pen exists (ordinary context) for the existential statement.


Concept / Approach:
If Erasers are disjoint from Papers and Pens are within Papers, then Erasers and Pens are disjoint (I). Also, if any pen exists, it is a paper, so at least some papers are pens (II).


Step-by-Step Solution:

I) Since Pens ⊆ Papers and Erasers ∩ Papers = ∅, it follows Erasers ∩ Pens = ∅ — no eraser is a pen.II) Pick any pen; it belongs to Papers, so 'Some papers are pens' holds.


Verification / Alternative check:
Venn diagrams depict Pens inside Papers and Erasers disjoint from Papers; both conclusions are immediate.


Why Other Options Are Wrong:
Options denying either I or II contradict the straightforward set relations.


Common Pitfalls:
Overlooking that an existential like 'some papers are pens' is justified by non-emptiness of Pens in typical exam logic.


Final Answer:
Both Conclusions I and II follow.

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