Syllogism — From universal inclusion plus particular membership Statements: 1) All stenographers are lazy. 2) Some men are stenographers. Conclusions: I) All lazy people are men. II) Some men are lazy. Select the conclusion(s) that must follow.

Difficulty: Easy

Correct Answer: Only Conclusion II follows

Explanation:


Introduction / Context:
The problem pairs a universal inclusion with an existential statement to test whether you can derive a necessary existential consequence while rejecting an overgeneralized universal converse.


Given Data / Assumptions:

  • All Stenographers ⊆ Lazy.
  • Some Men ⊆ Stenographers (i.e., there exists at least one man who is a stenographer).


Concept / Approach:
From the existence of at least one man who is a stenographer, and the fact that all stenographers are lazy, it follows that some men are lazy. However, claiming that all lazy people are men reverses and enlarges the set relation without support.


Step-by-Step Solution:

Step 1: Pick an element x such that x ∈ Men and x ∈ Stenographers (from “Some men are stenographers”).Step 2: Since Stenographers ⊆ Lazy, x ∈ Lazy.Step 3: Therefore, “Some men are lazy” holds — Conclusion II is true.Step 4: Conclusion I (“All lazy people are men”) is a converse generalization; nothing rules out lazy women or lazy non-men, so it does not follow.


Verification / Alternative check:
Construct a world with lazy students, lazy women, and lazy men; the premises remain true, but not all lazy people are men. This shows I is not necessary.


Why Other Options Are Wrong:

  • Only I follows: overgeneralization.
  • Both follow: includes the invalid I.
  • Neither follows: ignores the guaranteed existential in II.


Common Pitfalls:
Assuming that a subset relation can be flipped (converse error) or that one example proves a universal claim.


Final Answer:
Only Conclusion II follows.

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