Read the following statements about stenographers, lazy people, and men. Assume that both statements are true and then decide which conclusions definitely follow. Statement 1: All stenographers are lazy. Statement 2: Some men are stenographers. Conclusions: I. All lazy people are men. II. Some men are lazy.

Difficulty: Medium

Correct Answer: Only conclusion II follows.

Explanation:


Introduction / Context:
This question is another example of syllogism involving three sets: stenographers, lazy people, and men. The statements define how these sets are related, and you must find which conclusions are logically forced. Here, one statement is universal, and the other is particular. The problem checks whether you can correctly derive consequences from these and avoid reversing or overgeneralising them.


Given Data / Assumptions:
- Statement 1: All stenographers are lazy. Every member of the stenographer set is inside the lazy set. - Statement 2: Some men are stenographers. At least one man is a stenographer. - We are not told that all men are stenographers or that all lazy people are stenographers. - Conclusions I and II must be tested on this limited information.


Concept / Approach:
When we read All stenographers are lazy, we understand it as set inclusion: stenographers are a subset of lazy people. The statement Some men are stenographers places at least one man inside the stenographer set. From this, we can trace that man into the lazy set, because all stenographers are lazy. To validate a conclusion, we check if it holds in every possible configuration consistent with the statements. If a conclusion states more than what is guaranteed, it must be rejected.


Step-by-Step Solution:
Step 1: From Statement 2, there is at least one person who is both a man and a stenographer. Call this person X. Step 2: From Statement 1, every stenographer is lazy. Therefore, X, who is a stenographer, is also lazy. So X is a man and lazy, which directly implies that some men are lazy. Step 3: This confirms Conclusion II as correct, because it is exactly what we have deduced: there exists at least one man who is lazy. Step 4: Now examine Conclusion I, which states that all lazy people are men. This is much stronger than anything given. We only know that stenographers are lazy and that at least one stenographer is a man. There can be lazy women, lazy children, or lazy people in general who are not men and not stenographers. The statements do not restrict all lazy people to the group of men. Step 5: Since it is easy to imagine lazy people who are not men, and the statements do not rule them out, Conclusion I does not logically follow.


Verification / Alternative check:
As a quick verification, suppose there are 100 lazy people, of whom only 10 are stenographers and 5 of these stenographers are men. The remaining 90 lazy people could be women or children. In this scenario, all stenographers are still lazy and some men are stenographers, so the statements are true. However, it is clearly false that all lazy people are men. This concrete example reinforces that Conclusion I is invalid, while Conclusion II remains valid.


Why Other Options Are Wrong:
- Options that include Conclusion I assume that every lazy person must be male, which is not supported by the data. - The option that includes both conclusions fails because one of them clearly overstates the information given. - The option that rejects both conclusions ignores the direct chain from men to stenographers to lazy people that proves Conclusion II. - The cannot be determined option is incorrect, because we can definitely say that some men are lazy.


Common Pitfalls:
A common mistake is to reverse the universal statement and read All lazy people are stenographers or All lazy people are men from the given statements. Another error is to think that because a specific example exists, all members of a broader group must share the same property. In syllogism, you must always respect the direction and strength of each statement and avoid adding hidden assumptions.


Final Answer:
Thus, only the second conclusion is logically forced, so the correct answer is Only conclusion II follows.

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