Question:medium

Choose the set of three statements where the third statement can be logically derived from the preceding two.
Statements:
1. All boys need books.
2. All girls need books.
3. Punjabis are girls.
4. Some Punjabis need book.
5. All boys are girls.
6. Some boys are Punjabis.
The set of statements is:

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

Statement 5 places every boy inside the girls group, and statement 2 places every girl inside the 'needs books' group.

Chaining these two universal statements through the shared middle term 'girls' means every boy, being a girl, also needs books, giving statement 1, 'All boys need books', directly.

The other combinations either drag in Punjabis without a proper chain connecting them to the stated conclusion, or only support a partial 'some' conclusion rather than the universal claim being tested.

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

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Approach Solution -2

Statement 5, "All boys are girls," and statement 2, "All girls need books," are both universal affirmative statements, all B are G, and all G are N. This is a classic chained pattern in syllogistic logic, two universal affirmatives sharing a middle term validly combine into a third universal affirmative. Let's check each option against this:

  1. 5, 4, 1: Statement 4 is a particular statement about Punjabis needing books, it shares no common middle term with statement 5's boys-girls relationship, so no valid chain forms toward statement 1.
  2. 2, 5, 3: Statements 2 and 5 do chain validly through the middle term "girls," but the conclusion offered, statement 3 about Punjabis, introduces a term absent from both premises, breaking the valid pattern.
  3. 6, 5, 3: Statement 6 is a particular statement, not universal, "some boys are Punjabis," so it cannot combine with statement 5 to validly produce the universal claim in statement 3.
  4. 5, 2, 1: Statements 5 and 2 are both universal affirmatives sharing the middle term "girls," chaining them, all B are G and all G are N, validly yields all B are N, exactly statement 1.

The universal-plus-universal chain through a shared middle term applies cleanly only to statements 5 and 2, producing statement 1 as the valid conclusion.

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

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