UPSC CSE Prelims 2017
Conclusions:
The statement "All painters are poets" establishes that the set of painters is a subset of the set of poets. The statement "X is a poet" places X within the larger set of poets.
From these premises, it cannot be definitively concluded whether X belongs to the subset of painters or to the group of poets who are not painters. Therefore, neither conclusion I (X is a painter) nor conclusion II (X is not a painter) can be individually deduced with certainty.
However, conclusions I and II are a complementary pair. Logically, X must either be a painter or not be a painter. These two possibilities are mutually exclusive and exhaustive. Consequently, while the specific truth of either conclusion cannot be ascertained, one of them must necessarily be true. This constitutes an 'either-or' case.
Option (a) Only conclusion I follows: This is incorrect. The fact that X is a poet does not automatically imply X is a painter. X could be a poet who does not belong to the subset of painters.
Option (b) Only conclusion II follows: This is incorrect. The statements do not provide grounds to definitively state that X is not a painter. X could be a painter, as painters are included within the group of poets.
Option (d) Neither I nor II follows: This is incorrect. While neither conclusion can be individually established with certainty, the two conclusions (X is a painter, X is not a painter) represent a complete dichotomy. One of them must be true, even if which one is unknown based on the given premises.