Question

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: 
 

• A. 5, 4, 1
• B. 2, 5, 3
• C. 6, 5, 3
• D. 5, 2, 1

Hint:

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).

Answer 1

The Correct Option is D

The correct set is (D) — statements 5, 2, and 1.
Reasoning:
(5) “All boys are girls” — universal affirmative linking boys to girls.
(2) “All girls need books” — universal affirmative linking girls to books.
(1) “All boys need books” — this follows logically from (5) and (2) by the transitive property of syllogisms: Boys $\subset$ Girls and Girls $\subset$ Book-needers $\Rightarrow$ Boys $\subset$ Book-needers.

This set is internally consistent and directly connected through a common chain of reasoning. Other groupings fail because they either introduce unrelated categories or contain statements not derivable from the others. 
 

Answer 2

The question again gives six statements and asks which group of three forms a valid logical chain. Let's test each option using the standard rule that "All A are B" plus "All B are C" gives "All A are C":

1. 5, 4, 1 (All boys are girls; Some Punjabis need books; All boys need books): Statement 4 talks about Punjabis, a group not connected to "boys" by any other statement in this set, so it cannot combine with statement 5 to produce statement 1 in a valid way.
2. 2, 5, 3 (All girls need books; All boys are girls; Punjabis are girls): Statements 2 and 5 do combine validly to give "All boys need books", but that conclusion is not among these three statements; statement 3 introduces Punjabis, which is not derived from combining 2 and 5. So this set is not an internally complete chain.
3. 6, 5, 3 (Some boys are Punjabis; All boys are girls; Punjabis are girls): While statement 5 and statement 6 both mention boys, and statement 3 mentions Punjabis and girls, there is no single rule that ties all three into one continuous logical statement, unlike a straightforward two-premise-to-conclusion chain.
4. 5, 2, 1 (All boys are girls; All girls need books; All boys need books): Statement 5 places "boys" entirely inside "girls". Statement 2 places "girls" entirely inside "book-needers". Chaining these two universal statements together, boys inside girls and girls inside book-needers, necessarily means boys are inside book-needers too, which is precisely statement 1. This is the standard valid syllogism form, sometimes called Barbara: All A are B, All B are C, therefore All A are C.

Only the fourth grouping is a complete, self-contained chain where the third statement is the direct logical consequence of the first two.

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

Answer 3

Thinking of "boys," "girls," and "book-needers" as nested circles, where "All X are Y" means the X circle is drawn entirely inside the Y circle, let's check whether each option's three statements can be drawn as one consistent nested picture where the third is forced by the first two:

1. 5, 4, 1 (All boys are girls; Some Punjabis need books; All boys need books): Statement 5 draws the boys circle entirely inside the girls circle, but statement 4 introduces a separate Punjabis circle that has no drawn connection to the boys circle at all, so it cannot be combined with statement 5 to force statement 1.
2. 2, 5, 3 (All girls need books; All boys are girls; Punjabis are girls): Statements 2 and 5 do combine to nest boys inside girls inside book-needers, which would force "All boys need books," but that resulting statement is not one of the three listed here, statement 3 instead introduces a separate Punjabis circle nested inside girls, which is not something statements 2 and 5 force on their own.
3. 6, 5, 3 (Some boys are Punjabis; All boys are girls; Punjabis are girls): These three circles, boys, girls, Punjabis, overlap and nest in various ways, but there is no single two-statement nesting here that forces the third statement as its direct and necessary consequence.
4. 5, 2, 1 (All boys are girls; All girls need books; All boys need books): Drawing boys entirely inside girls, statement 5, and girls entirely inside book-needers, statement 2, automatically places boys entirely inside book-needers too, which is exactly statement 1. This is one single consistent nested picture where the third statement is forced directly by the first two.

Only the fourth grouping draws as one consistent set of nested circles where the third statement is the forced, necessary result of nesting the first two.

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