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Chain reasoning with two universals: Given 'Every minister is a student' and 'Every student is inexperienced', determine which conclusions — (I) 'Every minister is inexperienced' and (II) 'Some inexperienced are students' — are necessarily true.

Difficulty: Easy

Correct Answer: Both I and II follow

Explanation:

Given data

  • Premise 1: Minister ⊆ Student.
  • Premise 2: Student ⊆ Inexperienced.
  • Test: (I) Minister ⊆ Inexperienced. (II) Some Inexperienced are Students.

Concept/Approach

Subset chaining: if A ⊆ B and B ⊆ C, then A ⊆ C. For (II), if there exists at least one student (a standard assumption in these items), that student is inexperienced, yielding a 'Some' statement.

Step-by-step evaluation

1) From Premise 1 and 2: Minister ⊆ Student ⊆ Inexperienced ⇒ Minister ⊆ Inexperienced ⇒ (I) holds.2) Existence: Since ministers exist in the scenario, there exists at least one student; therefore 'Some inexperienced are students' ⇒ (II) holds.

Verification

Draw nested sets: Minister inside Student, inside Inexperienced; conclusions are immediate.

Common pitfalls

  • Missing the existence cue that supports the 'Some' conclusion.

Final Answer
Both I and II follow.

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