Statements: a) All children are students. b) All students are players. Conclusions: I. All cricketers are students. II. All children are players. Select the option that must follow.
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AOnly conclusion I follows.
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BNeither conclusion I nor II follows.
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CBoth conclusions I and II follow.
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DOnly conclusion II follows.
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EData inadequate.
Answer
Correct Answer: Only conclusion II follows.
Explanation
Introduction / Context:This is the same transitivity pattern as similar items: two universal affirmatives chained to test whether a third inclusion necessarily holds.
Given Data / Assumptions:
- Children ⊆ Students.
- Students ⊆ Players.
Concept / Approach:Transitivity: If A ⊆ B and B ⊆ C, then A ⊆ C. Any conclusion about unrelated classes (e.g., Cricketers) is not entailed unless connected by premises.
Step-by-Step Solution:1) Chain: Children ⊆ Players ⇒ all children are players (Conclusion II true).2) “All cricketers are students” is unsupported; cricketers may or may not be students.
Verification / Alternative check:Construct a countermodel where Cricketers are non-students while all children are students and students are players. Premises hold; Conclusion I fails.
Why Other Options Are Wrong:Options asserting I or both are stronger than what premises license.
Common Pitfalls:Importing real-world knowledge (e.g., “students often play cricket”), which is irrelevant to formal entailment.
Final Answer:Only conclusion II follows.