Consider the given statements to be true and decide which of the given conclusions or assumptions can definitely be drawn from them. Statements: 1. All books are novels. 2. Some novels are poems. Conclusions: I. Some books are poems. II. Some poems are novels. Choose the option that correctly identifies which conclusion or conclusions logically follow from these statements.

Difficulty: Medium

Correct Answer: Only conclusion II follows

Explanation:


Introduction / Context:
This question involves three sets: books, novels, and poems. Two statements define relations between these sets. Your job is to check which of the given conclusions is forced by these relations and which is not.


Given Data / Assumptions:
Accept the following as true.

  • Statement 1: All books are novels.
  • Statement 2: Some novels are poems.
  • Conclusion I: Some books are poems.
  • Conclusion II: Some poems are novels.
  • “Some” means at least one.


Concept / Approach:
From “All books are novels” we know the Book set lies inside the Novel set. From “Some novels are poems” we know there is at least one element in the intersection of Novels and Poems. The key question is whether that element must necessarily be a book or not, and what we can surely say about poems and novels.


Step-by-Step Solution:

Step 1: Statement 1 places every book inside the Novel set; there may be novels that are not books. Step 2: Statement 2 says there exists at least one element that is both a novel and a poem. Step 3: Conclusion II says “Some poems are novels.” This is exactly restating statement 2 in another form, because if some novels are poems, then some poems are necessarily novels as well. Step 4: Conclusion I claims “Some books are poems.” For this to be forced, we would need to know that the novels that are poems come specifically from the Book subset of the Novel set. However, the statements allow the possibility that the novels which are poems are not books at all. Step 5: Because it is possible to draw a consistent diagram where no book is a poem but some novels are poems, conclusion I is not necessary.


Verification / Alternative check:
Draw Novels as a large set. Inside it, place a smaller subset called Books. Then mark a region of Novels that overlaps with Poems. That overlapping region can be drawn outside the Books subset, showing that some novels are poems while possibly no book is a poem. In this picture, conclusion II remains true but conclusion I fails. This shows only conclusion II is guaranteed.


Why Other Options Are Wrong:
Option A says only conclusion I follows, which is invalid as conclusion I is not forced. Option C says neither follows, ignoring that conclusion II is a direct restatement of statement 2. Option D says both follow, which overstates what can be deduced from the given information.


Common Pitfalls:
Many students assume that any attribute shared by novels will automatically apply to books because all books are novels. However, you must remember that books are only a subset of novels. Other novels may have properties that books do not share, so you cannot push every property back into the subset.


Final Answer:
The only conclusion that necessarily follows is conclusion II. Hence, the correct answer is “Only conclusion II follows.”

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