Statements : Every minister is a student. Every student is inexperienced.…

Concept: Two rules of categorical syllogisms (under the classical convention followed in these reasoning tests, which takes every stated category to have at least one member) are needed here. First, when the middle term is the predicate of one universal affirmative premise and the subject of another universal affirmative premise, the two combine into a universal affirmative conclusion linking the two end terms — this is the chain rule. Second, any universal affirmative statement "All P are Q" also converts, by limitation under this same convention, into the particular statement "Some Q are P".

Application:

1. The two premises are: every minister is a student, and every student is inexperienced. "Student" is the middle term — it is the predicate of the first premise and the subject of the second, exactly the arrangement the chain rule needs.

2. Applying the chain rule to this arrangement: every minister is a student, and every student is inexperienced, so every minister is inexperienced. This is exactly conclusion I.

3. The second premise alone — every student is inexperienced — is a universal affirmative statement. Applying the conversion-by-limitation rule (valid under the same convention) to it gives: some inexperienced (people) are students. This is exactly conclusion II.

Cross-check: picture the three groups nested inside one another — ministers inside students, students inside inexperienced. Every point in the ministers group automatically lies inside the inexperienced group, confirming the first conclusion; and since the students group has at least one member and lies entirely inside the inexperienced group, at least some inexperienced individuals must be students, confirming the second.

Result: both conclusions follow logically from the given statements.