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Q60 (CISF/2024) Science & Technology › Basic Science (Physics, Chemistry, Biology)

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?

Result
Your answer: —  ·  Correct: D

Explanation

To determine if the conclusions are certainly drawn, we use Venn diagrams:

  • Statement I (Some P are Q): There is an intersection between the sets P and Q.
  • Statement II (Every R is Q): Set R is a subset of set Q (R is entirely inside Q).

Analysis:

  1. Conclusion I (Some P are R): While R is inside Q and P overlaps with Q, the overlap between P and Q does not necessarily include any part of R. P could overlap with a portion of Q that is completely separate from R. Thus, this conclusion is not certainly true.
  2. Conclusion II (Every R is P): Since R only needs to be inside Q, and P only needs to overlap with Q, R could be entirely outside P or only partially overlap with it. Thus, this conclusion is also not certainly true.

Since neither conclusion is guaranteed to be true in all possible scenarios, the correct option is D.

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