In this set based reasoning question, two statements are given about papers, files and pens. Treat both statements as true and decide which of the conclusions, if any, logically follow: Statements: (I) All paper are files. (II) Some files are pens. Conclusions: (I) No paper is a pen. (II) Some papers are pens.

Introduction / Context:
This problem checks your understanding of partial and complete set relationships. Two statements describe how the sets paper, files and pens are related. You must decide whether either of two conflicting conclusions about papers and pens is forced by those statements.

Given Data / Assumptions:

• Statement I: All paper are files.
• Statement II: Some files are pens.
• Conclusion I: No paper is a pen.
• Conclusion II: Some papers are pens.
• Paper refers to all sheets treated as a single set; files and pens are abstract sets as well.

Concept / Approach:
All paper are files means that the set paper lies entirely inside the set files. Some files are pens means there is at least one element that is both a file and a pen. However, the statements do not specify whether the paper objects are inside or outside that overlapping region of files and pens. To test each conclusion, we must see whether the statements force paper to avoid pens completely or force at least some paper to fall into the overlap with pens.

Step-by-Step Solution:
Step 1: Draw the set of files and place the set paper completely inside it to represent all paper are files. Step 2: Represent some files are pens by drawing the set pens so that it intersects the set files in a non empty region. Step 3: Check conclusion I, no paper is a pen. This would require that the entire set paper lies in the part of files that is outside pens. Step 4: It is possible to draw the diagram so that paper lies entirely outside the overlapping region, satisfying the statements and making conclusion I true. But it is also possible to place some or all of paper inside the overlap between files and pens, still satisfying the statements. Step 5: Check conclusion II, some papers are pens. This would require that at least part of the set paper lies in the overlap with pens. Step 6: As noted, there are valid diagrams where no paper lies in the overlap and diagrams where some paper lies in it. Therefore, the statements do not force either extreme; both kinds of arrangements are possible.

Verification / Alternative check:
Construct two examples. In example one, let files be {f1, f2, f3}, pens be {f3, p1}, and paper be {f1}. Then all paper (f1) are files, and some files (f3) are pens. Here, no paper is a pen, so conclusion I is true and conclusion II is false. In example two, let paper be {f3} instead, keeping the other sets the same. Now paper (f3) is both a file and a pen, so some papers are pens, conclusion II is true and conclusion I is false. The fact that both patterns are possible shows that neither conclusion is logically forced by the statements alone.

Why Other Options Are Wrong:
Option A asserts conclusion I, but we have seen a situation where conclusion II holds instead and the statements remain true. Option B asserts conclusion II, but example one shows that conclusion II can fail. Option D claims both conclusions follow, which is impossible because the conclusions contradict each other. Option E suggests an exclusive either or, but the logical task is to identify which conclusions must always hold, and the answer is that neither is guaranteed.

Common Pitfalls:
A typical mistake is to assume that if some files are pens and all paper are files, then automatically some papers are pens. This ignores the possibility that paper occupies the non overlapping part of files. Another pitfall is to jump to the opposite extreme and assume that paper must avoid pens, making conclusion I seem attractive. Always test with small concrete examples before deciding.

Final Answer:
The correct logical result is that neither conclusion I nor conclusion II follows from the given statements.