Question:
Given below are two statements
Statement I: Some men are great.
Statement II: Some men are wise.
Conclusion I: Men are either great or wise.
Conclusion II: Some men are neither great nor wise.
In light of the above statements, choose the correct answer from the options given below:
Given below are two statements
Statement I: Some men are great.
Statement II: Some men are wise.
Conclusion I: Men are either great or wise.
Conclusion II: Some men are neither great nor wise.
In light of the above statements, choose the correct answer from the options given below:
Statement I: Some men are great.
Statement II: Some men are wise.
Conclusion I: Men are either great or wise.
Conclusion II: Some men are neither great nor wise.
In light of the above statements, choose the correct answer from the options given below:
Show Hint
In syllogisms, a conclusion is only valid if it is true in all possible Venn diagram scenarios. If you can draw even one scenario where a conclusion is false, that conclusion is invalid.
Updated On: Aug 13, 2026
- Only conclusion I is valid.
- Only conclusion II is valid.
- Both the conclusions are valid.
- Neither of the conclusions are valid.
Show Solution
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The Correct Option is D
Solution and Explanation
Step 1: Understanding the Concept:
Syallogistic and categorical reasoning requires determining whether conclusions follow necessarily from given premises, regardless of real-world assumptions.
We use Venn diagrams to test the validity of these conclusions.
Detailed Explanation:
Let us represent the premises using sets:
- Statement I: "Some men are great." This means the intersection of the set of 'Men' (\(M\)) and 'Great' (\(G\)) is non-empty (\(M \cap G \neq \emptyset\)).
- Statement II: "Some men are wise." This means the intersection of the set of 'Men' (\(M\)) and 'Wise' (\(W\)) is non-empty (\(M \cap W \neq \emptyset\)).
- Note that there is no specified relationship between 'Great' (\(G\)) and 'Wise' (\(W\)).
Let us evaluate the conclusions:
- Conclusion I: "Men are either great or wise."
This implies that every member of the set 'Men' must belong to either set \(G\) or set \(W\) (i.e., \(M \subseteq G \cup W\)).
This is invalid because there can be men who are neither great nor wise.
- Conclusion II: "Some men are neither great nor wise."
While this statement is often true in the real world, we must evaluate if it is logically necessary based *only* on the premises.
It is possible to construct a valid Venn diagram where the union of the sets 'Great' and 'Wise' completely covers the set 'Men' (meaning every man is either great, wise, or both), while still satisfying the "some" conditions of both premises.
Because we can construct a valid scenario where Conclusion II is false, it does not follow necessarily from the premises.
Therefore, neither conclusion is logically valid.
Step 2: Final Answer:
Neither of the conclusions is valid, corresponding to Option (D).
Syallogistic and categorical reasoning requires determining whether conclusions follow necessarily from given premises, regardless of real-world assumptions.
We use Venn diagrams to test the validity of these conclusions.
Detailed Explanation:
Let us represent the premises using sets:
- Statement I: "Some men are great." This means the intersection of the set of 'Men' (\(M\)) and 'Great' (\(G\)) is non-empty (\(M \cap G \neq \emptyset\)).
- Statement II: "Some men are wise." This means the intersection of the set of 'Men' (\(M\)) and 'Wise' (\(W\)) is non-empty (\(M \cap W \neq \emptyset\)).
- Note that there is no specified relationship between 'Great' (\(G\)) and 'Wise' (\(W\)).
Let us evaluate the conclusions:
- Conclusion I: "Men are either great or wise."
This implies that every member of the set 'Men' must belong to either set \(G\) or set \(W\) (i.e., \(M \subseteq G \cup W\)).
This is invalid because there can be men who are neither great nor wise.
- Conclusion II: "Some men are neither great nor wise."
While this statement is often true in the real world, we must evaluate if it is logically necessary based *only* on the premises.
It is possible to construct a valid Venn diagram where the union of the sets 'Great' and 'Wise' completely covers the set 'Men' (meaning every man is either great, wise, or both), while still satisfying the "some" conditions of both premises.
Because we can construct a valid scenario where Conclusion II is false, it does not follow necessarily from the premises.
Therefore, neither conclusion is logically valid.
Step 2: Final Answer:
Neither of the conclusions is valid, corresponding to Option (D).
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