In the following logical reasoning problem, two statements are given about men, saints and sinners. You must treat both statements as true and then decide which of the given conclusions, if any, logically follows from them: Statements: (I) Men are sinners. (II) Saints are men. Conclusions: (I) Saints are sinners. (II) Sinners are saints.

Difficulty: Medium

Correct Answer: Conclusion I follows

Explanation:


Introduction / Context:
This question tests basic syllogism skills. You are given two simple universal statements about men, saints and sinners. Your task is to see which conclusion necessarily follows from these statements, assuming they are perfectly true, even if they disagree with everyday beliefs or moral views.


Given Data / Assumptions:

  • Statement I: Men are sinners.
  • Statement II: Saints are men.
  • Conclusion I: Saints are sinners.
  • Conclusion II: Sinners are saints.
  • All terms refer to sets or groups of people.


Concept / Approach:
In syllogism, a statement like men are sinners means every member of the set men belongs to the set sinners. Similarly, saints are men means every saint belongs to the set men. By combining such subset relations, we can see what other subset relations must hold. However, we must be careful not to reverse the direction of inclusion, because that usually creates invalid conclusions.


Step-by-Step Solution:
Step 1: Translate statement I into set language: all men are sinners. The set of men is completely contained inside the set of sinners. Step 2: Translate statement II: all saints are men. The set of saints is completely contained inside the set of men. Step 3: Combine the two: if all saints are men and all men are sinners, then every saint is also a sinner. This is a direct chain of inclusion: saints ⊂ men ⊂ sinners. Step 4: Therefore conclusion I, saints are sinners, must be true whenever both statements are true. Step 5: Consider conclusion II, sinners are saints. This would mean the set of sinners is contained inside the set of saints. The given statements do not say this. They only say saints are a subset of men and men are a subset of sinners. Step 6: It is possible to have many sinners who are not saints at all. So conclusion II does not logically follow.


Verification / Alternative check:
Imagine an example. Suppose there are 100 men, all of whom are sinners. Out of these, only 10 are saints. Then every saint is a man and every man is a sinner. That matches the statements. In this picture, the 10 saints are sinners, so conclusion I holds. But there are 90 other sinners who are not saints, so it is false that all sinners are saints. This shows that conclusion II is not forced by the statements.


Why Other Options Are Wrong:
Option B claims only conclusion II follows, which is incorrect because conclusion II can easily be false while the statements remain true. Option C says neither conclusion follows, but we have seen that conclusion I must always hold. Option D says both conclusions follow, which wrongly includes conclusion II. Option E suggests that exactly one of the two follows without specifying, but the question and option wording require you to identify the specific correct conclusion, which is conclusion I only.


Common Pitfalls:
A common mistake is to mix up all A are B with all B are A. From men are sinners you cannot say all sinners are men. Similarly, from saints are men you cannot say all men are saints. Always keep track of the direction of the arrow in subset relations. Drawing a simple Venn diagram often helps to avoid this confusion.


Final Answer:
The correct logical result is that only conclusion I follows, that is, saints are sinners.

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