Q. If “No scientists are philosophers” is true, which one of the following propositions is true ?
a) Some non-philosophers are not non-scientists.
b) Some philosophers are scientists.
c) No non-philosophers are scientists.
d) All scientists are philosophers.
Correct Answer: a) Some non-philosophers are not non-scientists.
Question from UPPSC Prelims CSAT 2025
Explanation:
Let S = scientists and P = philosophers. The premise “No scientists are philosophers” means S ∩ P = ∅, equivalently All S are non-P.
Evaluate options:
– Option 2: “Some philosophers are scientists” asserts P ∩ S ≠ ∅, directly contradicting the premise. False.
– Option 4: “All scientists are philosophers” says S ⊆ P, the opposite of the premise (which says S ⊆ non-P). False.
– Option 3: “No non-philosophers are scientists” means non-P ∩ S = ∅, i.e., S ⊆ P (again, the exact opposite). False.
– Option 1: “Some non-philosophers are not non-scientists” simplifies to “Some non-P are S” (since not non-scientists = scientists), i.e., Some S are non-P. This is consistent with the premise (indeed, it follows if at least one scientist exists). It is the only option compatible with the given statement.
Therefore, Option 1 is true.
