Question:medium

Given statements:
1. All boys need books.
2. All girls need books.
3. Punjabis are girls.
4. Some Punjabis need books.
5. All boys are girls. 6. Some boys are Punjabis.
The set of statements is: 
 

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In syllogism-type grouping, check if two statements logically imply the third. A valid set will often form a direct chain (A→B, B→C, hence A→C).
Updated On: Jul 15, 2026
  • 5, 4, 1
  • 2, 5, 3
  • 6, 5, 3
  • 5, 2, 1
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The Correct Option is D

Approach Solution - 1

Step 1: Look for two universal ("All") statements that share a common middle term; here statement 5 ("All boys are girls") and statement 2 ("All girls need books") share the term "girls".

Step 2: Apply the chain rule: All A are B + All B are C \( \Rightarrow \) All A are C, giving Boys \( \subset \) Girls and Girls \( \subset \) Book-needers \( \Rightarrow \) Boys \( \subset \) Book-needers, which is exactly statement 1.

Step 3: None of the other option sets (5,4,1 / 2,5,3 / 6,5,3) contain all three of a matching premise pair plus its exact conclusion together.

Conclusion: The valid set is 5, 2, 1.
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Approach Solution -2

Treating "All A are B" as a mathematical inclusion relation, written \( A \subseteq B \), lets us check each option using the transitive property of inclusion: if \( A \subseteq B \) and \( B \subseteq C \), then it always follows that \( A \subseteq C \). Let's test each option against this property:

  1. 5, 4, 1 (All boys are girls; Some Punjabis need books; All boys need books): Statement 5 gives \( \text{Boys} \subseteq \text{Girls} \), but statement 4 is about Punjabis, not Girls, so there is no shared middle set to chain with statement 5, and the transitive property cannot be applied here.
  2. 2, 5, 3 (All girls need books; All boys are girls; Punjabis are girls): Statement 2 gives \( \text{Girls} \subseteq \text{Book-needers} \) and statement 5 gives \( \text{Boys} \subseteq \text{Girls} \), which do chain by transitivity into \( \text{Boys} \subseteq \text{Book-needers} \), but that conclusion is not statement 3, which instead talks about Punjabis, an unrelated chain.
  3. 6, 5, 3 (Some boys are Punjabis; All boys are girls; Punjabis are girls): Statement 6 is only a partial "Some" relation, not a full inclusion, so it cannot be chained using the transitive property, which requires full "All" inclusion relations on both sides.
  4. 5, 2, 1 (All boys are girls; All girls need books; All boys need books): Statement 5 gives \( \text{Boys} \subseteq \text{Girls} \) and statement 2 gives \( \text{Girls} \subseteq \text{Book-needers} \). By the transitive property of inclusion, this directly chains to \( \text{Boys} \subseteq \text{Book-needers} \), which is exactly statement 1.

Only the fourth grouping satisfies the transitive property of inclusion in full, where the third statement is the direct mathematical consequence of chaining the first two.

Therefore, the correct answer is 5, 2, 1.

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