Two Statements followed by four Conclusions are given below. You have to take the Statements to be true even if they seem, to be at variance from the commonly known facts. Read all the Conclusions and then decide which of the given Conclusions logically follows/follow from the Statements, disregarding the commonly known facts:
Statement-1: All pens are books.
Statement-2: No chair is a pen.
Conclusion-I: All chairs are books.
Conclusion-II: Some chairs are pens.
Conclusion-III: All books are chairs.
Conclusion-IV: No chair is a book.
Which one of the following is correct?

The correct answer is None of the Conclusions follows.

Let us analyze the given statements step-by-step using logic and Venn diagrams to see why none of the conclusions logically follow.

Step 1: Analyze the Statements
1. Statement-1: All pens are books.
This means that the set of "pens" is entirely contained within the set of "books". We can represent this as:
$\mathrm{Pens}\subseteq \mathrm{Books}$
2. Statement-2: No chair is a pen.
This means that the set of "chairs" and the set of "pens" have no elements in common. They are completely disjoint:
$\mathrm{Chairs}\cap \mathrm{Pens}=\varnothing$

Step 2: Evaluate the Conclusions
Based on the statements, the set of "books" contains all "pens", but it can also contain other elements. The set of "chairs" is disjoint from "pens", but it may or may not overlap with the remaining part of "books" (i.e., books that are not pens).
Let us check each conclusion against these relationships:

Conclusion-I: All chairs are books.
Since "chairs" only need to be disjoint from "pens", they can be completely outside the set of "books". There is no requirement for any chair to be a book. Therefore, this conclusion does not logically follow.

Conclusion-II: Some chairs are pens.
Statement-2 explicitly states that "No chair is a pen." This directly contradicts Conclusion-II. Therefore, this conclusion does not logically follow.

Conclusion-III: All books are chairs.
Since all pens are books, and no pen can be a chair, it is impossible for all books to be chairs (specifically, the books that are pens cannot be chairs). Therefore, this conclusion does not logically follow.

Conclusion-IV: No chair is a book.
While it is possible for chairs and books to be completely disjoint, it is also possible for some chairs to be books (in the region of books that are not pens) without violating any statements. Since we cannot say with certainty that no chair is a book, this conclusion does not logically follow.

Conclusion:
Since none of the four conclusions logically follow from the given statements, the correct option is None of the Conclusions follows.