Under the traditional categorical-logic convention used in this question…

In traditional categorical logic, a universal affirmative proposition “All S are P” places the entire non-empty class S inside class P. Its universal negative “No S is P” and particular negative “Some S is not P” contradict that inclusion, while subalternation gives “Some S is P” as true.

Application

1. For (i), “No students are intelligent” contradicts the inclusion of every student in the intelligent class, so (i) is false.

2. For (ii), because the student class is assumed non-empty, at least one student exists and is intelligent; hence (ii) is true.

3. For (iii), “Some students are not intelligent” asserts a student outside the intelligent class, contradicting “All students are intelligent”; hence (iii) is false.

Cross-check and contrast

In set terms, Students is a non-empty subset of Intelligent. Therefore at least one student is intelligent, and no student lies outside the intelligent class. This confirms that the false statements are (i) and (iii).

• “(i) and (ii)” includes (ii), which follows under the non-empty-class convention.

• “(i) and (iii)” contains exactly the two statements that contradict the universal affirmative.

• “(ii) and (iii)” includes (ii), which is true under the convention.

• “(i) only” omits (iii), which also contradicts the universal statement.