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.

To determine which of the conclusions logically follow, let's analyze the given statements step-by-step using Venn diagrams and logical deductions:

1. "All Rose are Pink."
This means the entire set of Rose is contained within the set of Pink. Formally, $R\subseteq P$.

2. "Only a few Black is Pink."
This statement implies two things:
- Some Black are Pink ($B\cap P\ne \varnothing$).
- Some Black are NOT Pink ($B\setminus P\ne \varnothing$).

3. "No White is Rose."
This means there is no intersection between the set of White and the set of Rose ($W\cap R=\varnothing$).

Now let's evaluate each conclusion:

Conclusion I: "Some Rose is Black."
From the statements, we know that all Rose are Pink, and some Black are Pink. However, there is no direct relationship or intersection defined between Rose and Black. Rose and Black may or may not overlap. Since this overlap is not definite, the conclusion "Some Rose is Black" does not logically follow.

Conclusion II: "Some Pink can never be White."
We know from the first statement that all Rose are Pink. This means the Rose set is a part of the Pink set.
We also know from the third statement that no White is Rose (i.e., the Rose set and the White set are completely disjoint).
Since all Rose are Pink and no Rose can be White, the portion of Pink that is Rose can never be White. Thus, there is definitely a part of Pink (specifically, the Rose part) that can never be White. Therefore, this conclusion logically follows.

Consequently, only conclusion II follows.