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. Give answer-

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.

Correct Answer: If only conclusion II follows

Let us analyze the given statements step-by-step using standard syllogism and set theory rules:

Given Statements:
1. All Rose are Pink: The entire set of Rose is contained within the set of Pink.
2. Only a few Black is Pink: This means "Some Black is Pink" and "Some Black is NOT Pink". Thus, there is an intersection between Black and Pink, but Black is not entirely inside Pink.
3. No White is Rose: There is zero overlap between the set of White and the set of Rose.

Evaluation of Conclusions:

Conclusion I: Some Rose is Black
From the statements, all Roses are in Pink, and some Black is in Pink. However, there is no direct relationship or definite overlap given between the set of Rose and the set of Black. Rose and Black may or may not overlap. Since it is not definite, Conclusion I does not follow.

Conclusion II: Some Pink can never be White
We know that "All Rose are Pink", which means all elements of Rose are inside the Pink set. We also know that "No White is Rose", meaning no element of Rose can ever be White. Therefore, the portion of Pink that contains Rose can never be White. Thus, at least that part of Pink (the Rose part) can never be White. Hence, "Some Pink can never be White" is a definite truth and logical certainty. Therefore, Conclusion II follows.

Consequently, only conclusion II logically follows from the given statements.