In each question below, some statements are given followed by two conclusions numbered I and II. You have to take the given statements to be true even if they seem to be at variance with commonly known facts. Read all the conclusions and then decide which of the given conclusion logically follows from the given statements, disregarding commonly known facts. Giveanswer-

Statements:
All Rose are Pink.
Only a few Black is Pink.
No White is Rose.

Conclusions:
I. Some Rose is Black.
II. Some Pink can never be White.

The correct option is If only conclusion II follows.

Let us analyze the statements step-by-step using logical deductions and Venn diagram concepts:

1. Analyze the Statements:
- "All Rose are Pink": The entire set of Rose is contained within the set of Pink.
- "Only a few Black is Pink": This statement implies two things: "Some Black is Pink" and "Some Black is not Pink".
- "No White is Rose": There is no intersection between the set of White and the set of Rose. That is, no Rose can be White, and no White can be Rose.

2. Evaluate Conclusion I ("Some Rose is Black"):
- The statements tell us that all Rose are Pink and only a few Black is Pink. However, there is no direct connection established between Rose and Black.
- While it is possible for some Rose to be Black, it is not a definite or necessary conclusion. Therefore, Conclusion I does not logically follow.

3. Evaluate Conclusion II ("Some Pink can never be White"):
- From the first statement, we know that "All Rose are Pink". This means the entire set of Rose lies inside the Pink set.
- From the third statement, we know that "No White is Rose", which also means no Rose can be White.
- Since all Rose are a part of Pink, that specific portion of Pink which is Rose can never be White.
- Thus, there is definitely a portion of Pink (specifically, the Rose part) that can never be White. Therefore, Conclusion II is logically true and follows definitely.

Conclusion:
Only conclusion II logically follows from the given statements.