Statements: • All children are students. • All students are players. Conclusions: I. All cricketers are students. II. All children are players. Choose the option that logically follows from the statements.

Introduction / Context:
Questions of this form test classic categorical syllogism reasoning using inclusion (subset) chains. We are given two universal affirmative statements and asked which conclusion must hold in every model built from those premises.

Given Data / Assumptions:

• Premise 1: All children are students (Children ⊆ Students).
• Premise 2: All students are players (Students ⊆ Players).
• Standard syllogism rules apply; terms refer to non-empty sets unless emptiness is explicitly relevant. No unstated relationships are assumed beyond the premises.

Concept / Approach:
For universal statements of the form “All A are B”, we can chain subsets: if A ⊆ B and B ⊆ C, then A ⊆ C. Conclusions must be entailed solely by this logic, not by common knowledge about sports or everyday meaning.

Step-by-Step Solution:
1) Chain the premises: Children ⊆ Students and Students ⊆ Players.2) By transitivity, Children ⊆ Players. So every child is necessarily a player.3) Examine Conclusion I: “All cricketers are students.” The premises mention Students and Players, not Cricketers. Cricketers could be a subset of Players, a disjoint set, or overlap in many ways. There is no necessary containment Cricketers ⊆ Students.4) Examine Conclusion II: “All children are players.” This is exactly the transitive result from Step 2, so it must follow.

Verification / Alternative check:
Construct a countermodel for Conclusion I: Let Students = {s1}, Players = {s1, p2}, Children = {s1}. Let Cricketers = {p2}. All premises hold, but not all cricketers are students, refuting Conclusion I.

Why Other Options Are Wrong:

• Only I: false, as shown by countermodel.
• Both I and II: false because I fails.
• Neither: false because II is true.
• “Data inadequate”: not applicable; the logic is determinate.

Common Pitfalls:
A common mistake is to treat “Players” as synonymous with “Cricketers.” The test uses abstract set relations; domain knowledge must not be injected. Another error is assuming reversals like Students ⊆ Children; universal statements do not imply converses.

Final Answer:
Only conclusion II follows.