Each of the questions below consists of several statements followed by two conclusions numbered I and II. You must consider the statements to be true even if they conflict with commonly known facts. Read all the conclusions and determine which of them logically follows from the given statements.

Statements:
Only a few Router are Switch.
Some Hub are Switch.
No Router is Hub.
Some Modem are Hub.
Conclusions:
I: Some Router are not Switch.
II: Some Modem being Router is a possibility.

Correct Answer: If both conclusions I and II follow.

Step-by-Step Explanation:

Let us analyze the given statements step-by-step and test the validity of each conclusion.

Given Statements:
1. Only a few Router are Switch.
This statement carries a dual meaning:
- Some Routers are Switches.
- Some Routers are NOT Switches.
2. Some Hub are Switch. (Some Hubs intersect with Switches)
3. No Router is Hub. (Routers and Hubs have no overlap / zero intersection)
4. Some Modem are Hub. (Some Modems intersect with Hubs)

Analysis of Conclusion I:
Conclusion I: Some Router are not Switch.
From Statement 1 ("Only a few Router are Switch"), by definition, it directly implies that there are some Routers which are definitely not Switches. Therefore, Conclusion I is a definite truth and logically follows.

Analysis of Conclusion II:
Conclusion II: Some Modem being Router is a possibility.
From the statements, we know that no Router is a Hub, and some Modems are Hubs. However, there is no direct negative restriction given between Modem and Router. The part of Modem that is not a Hub can overlap with Router without violating any of the given statements. Therefore, the possibility of some Modems being Routers exists. Thus, Conclusion II logically follows.

Since both conclusions I and II logically follow, the correct choice is If both conclusions I and II follow.