In the following question, consider the statements: I. All books are pens. II. All pens are tables. Based on these statements, decide which of the conclusions given below logically follow.

Difficulty: Easy

Correct Answer: Only conclusion I follows

Explanation:


Introduction / Context:
This question is a classic syllogism problem. We are given two categorical statements about classes of objects, such as books, pens and tables. The task is to determine which conclusions follow logically from the given statements without using outside knowledge. Syllogism questions are common in verbal and logical reasoning sections of competitive exams.


Given Data / Assumptions:

  • Statement I: All books are pens.
  • Statement II: All pens are tables.
  • Conclusion I: Some pens are tables.
  • Conclusion II: All tables are books.


Concept / Approach:
The standard way to handle such questions is to think in terms of sets. If all members of set A are inside set B, and all members of set B are inside set C, then set A is inside set C. From this, we can decide whether statements like "some" or "all" types of objects in one set belong to another. We must not assume that every table is necessarily a pen or book unless that is clearly stated or can be deduced from the given premises.


Step-by-Step Solution:
Step 1: Translate the statements into set language. All books are pens means the set of books is completely inside the set of pens. All pens are tables means the set of pens is completely inside the set of tables. Step 2: Combine the two statements. Since books are inside pens and pens are inside tables, it follows that books are also inside tables. We do not need this directly for the conclusions, but it tells us how the sets are nested. Step 3: Evaluate conclusion I: Some pens are tables. If all pens are tables, then clearly at least one pen (in fact every pen) is a table. Therefore, the statement "some pens are tables" is logically true. Conclusion I follows from the premises. Step 4: Evaluate conclusion II: All tables are books. We only know that pens are a subset of tables and books are a subset of pens. There is no information that every table must be a pen, or that every table must be a book. There may be tables that have nothing to do with pens or books. So "all tables are books" does not logically follow.


Verification / Alternative check:
Imagine a diagram. Draw a large circle for tables. Inside that, draw a smaller circle for pens, and inside pens an even smaller circle for books. This picture matches both statements: all books are pens and all pens are tables. Now look at the circles. Some pens are definitely inside the table circle, so conclusion I is true. However, there are parts of the table circle outside the pen circle and outside the book circle. Thus not all tables are books, and conclusion II is false.


Why Other Options Are Wrong:

  • Option b (only conclusion II) is wrong because conclusion II does not follow.
  • Option c (both) is wrong since only the first conclusion is valid.
  • Option d (neither) is wrong because conclusion I clearly follows.
  • Option e mixes statements that are partly true and partly false, and is not the format asked by the question.


Common Pitfalls:
Many learners reverse the direction of the statements. From "all books are pens" they incorrectly infer "all pens are books," which is not correct. Similar reversal happens with tables. Always remember that if all A are B, it does not mean all B are A. Only the inclusion A inside B is guaranteed, not the reverse inclusion.


Final Answer:
Only conclusion I follows, so option a is correct.

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