Difficulty: Easy
Correct Answer: Only conclusion I follows
Explanation:
Introduction / Context:
This question uses very simple statements about sets of men and monkeys to test your ability to draw direct logical consequences. You are told that no man is a monkey and that Hari is a man. From this, you must decide which conclusions concerning Hari and the set of men are logically compelled by the statements.
Given Data / Assumptions:
- Statement 1: No man is a monkey, meaning the sets men and monkeys are completely disjoint.
- Statement 2: Hari is a man, meaning Hari belongs to the set of men.
- Conclusion I: Hari is not a monkey, which claims that Hari does not belong to the set of monkeys.
- Conclusion II: All men are not Hari, which suggests that the set of men consists of individuals who are not equal to Hari, or that Hari is not identical to the entire set of men.
Concept / Approach:
We interpret the statements in set language. Let M represent the set of men and K represent the set of monkeys. Statement 1 says M ∩ K is empty. Statement 2 says Hari is an element of M. Using these, we check conclusions about Hari and about the structure of the set M. We must distinguish between what we can assert about this specific individual and what we can assert about the entire population of men.
Step-by-Step Solution:
Step 1: From Statement 2, Hari belongs to M, the set of men.
Step 2: From Statement 1, there is no element that belongs to both M and K. That is, no man is a monkey.
Step 3: Since Hari is in M and no member of M can be in K, Hari cannot belong to the set K of monkeys.
Step 4: Therefore, Hari is not a monkey, which directly supports Conclusion I.
Step 5: Now evaluate Conclusion II, which says all men are not Hari. This can be interpreted as saying that no man is identical to Hari except possibly Hari himself, or that the set of men is strictly larger than the singleton {Hari}.
Step 6: The original statements do not specify how many men there are. It is logically possible that Hari is the only man in the universe of discourse, in which case every man is Hari.
Step 7: Since the number of men is unknown, we cannot definitively say that all men are not Hari, so Conclusion II does not logically follow.
Verification / Alternative check:
Consider two possible worlds. In World A, suppose there are many men: Hari, Ram, and others. Here, it is true that not all men are Hari. In World B, suppose Hari is the only man. In that world, the statement "all men are not Hari" is false because the only man is Hari. Both worlds satisfy the original statements, but Conclusion II is false in World B. Thus, Conclusion II is not logically forced by the given information, while Conclusion I is true in every world because Hari is a man and no man is a monkey.
Why Other Options Are Wrong:
Option B chooses only Conclusion II, which is unsupported. Option C claims both conclusions follow, but as shown, Conclusion II is not logically necessary. Option D says neither conclusion follows, which is incorrect because Conclusion I follows directly and unambiguously from the statements. Option E is more of a commentary than a direct answer to which conclusion follows and does not match the required format of the problem.
Common Pitfalls:
Many students misread Conclusion II as if it were saying simply that Hari is not all men at once, which feels intuitively true, but logic requires checking whether any scenario consistent with the statements might make the conclusion false. Since we do not know how many men exist, we cannot rule out the case where Hari is the only man, and in that case the wording "all men are not Hari" becomes problematic. Always remember that existence or number of elements is important in these questions.
Final Answer:
The correct option is Only conclusion I follows, because we can definitely say that Hari is not a monkey, but we cannot draw conclusions about the entire set of men beyond what is explicitly stated.
Discussion & Comments