Consider the following Statements and Conclusions:
Statements :
- Mohan is a good sportsman.
- Sportsmen are healthy.
Conclusions :
- I. All healthy persons are sportsmen.
- II. Mohan is healthy.
Which one of the following is correct?
Only Conclusion I follows
Only Conclusion II follows
Both Conclusion I and Conclusion II follow
Neither Conclusion I nor Conclusion II follows
Answer is Wrong!
Answer is Right!
This question was previously asked in
UPSC CAPF – 2016
From statement (2), we know that the property of being ‘healthy’ applies to all ‘sportsmen’. Statement (1) tells us that Mohan is a ‘sportsman’. Since Mohan belongs to the category ‘sportsmen’, and all members of this category are ‘healthy’ according to statement (2), it logically follows that Mohan is ‘healthy’. Thus, Conclusion II is valid.
Conclusion I states: “All healthy persons are sportsmen.” This is the converse of statement (2). Statement (2) “All Sportsmen are Healthy” (S -> H) does not imply “All Healthy persons are Sportsmen” (H -> S). There can be healthy persons who are not sportsmen (e.g., a healthy artist or student). Therefore, Conclusion I does not follow logically.
Statement 1: Mohan ∈ Sportsmen
Statement 2: Sportsmen ⊆ Healthy Persons (All S are H)
From these, it follows that Mohan ∈ Healthy Persons. (Conclusion II)
The converse of “All S are H” is “All H are S”, which is not necessarily true.