Consider the following statements and conclusions:
- Statement I : Some P are Q.
- Statement II : Every R is Q.
Conclusion I : Some P are R.
Conclusion II : Every R is P.
Which of the above conclusions can be certainly drawn?
Conclusion I only
Conclusion II only
Both conclusions I and II
Neither conclusion I nor II
Answer is Wrong!
Answer is Right!
This question was previously asked in
UPSC CISF-AC-EXE – 2024
I: Some P are Q.
II: Every R is Q.
Conclusion I: Some P are R.
Conclusion II: Every R is P.
Statement II (Every R is Q) means that the set R is a subset of the set Q. Statement I (Some P are Q) means that the set P has at least one element in common with the set Q.
Conclusion I: Some P are R. This means the intersection of sets P and R is not empty.
Conclusion II: Every R is P. This means the set R is a subset of the set P.
Consider a scenario where the set P overlaps with Q, but the overlap region is entirely outside R. In this case, “Some P are Q” and “Every R is Q” hold true, but “Some P are R” is false, and “Every R is P” is false.
Since there exists a valid interpretation of the statements where both conclusions are false, neither conclusion can be certainly drawn from the given statements.