Logical deduction – library visitors are only students or teachers: Determine a valid pair. (i) Rajesh is in the library. (ii) Shiva is in the library. (iii) Rajesh is a student. (iv) Shiva may be a teacher.

Introduction / Context:The statement "Only students or teacher visit the library" means InLibrary ⇒ (Student ∨ Teacher). We can draw categorization conclusions from presence in the library.

Given Data / Assumptions:

• If a person is in the library, they must be a student or a teacher.

Concept / Approach:(i) asserts presence; thus (iii) is a valid specific instantiation. (ii) (iv) is also compatible, but the question asks for a definitive pair implied by the rule; (i) (iii) is a clean consequence.

Step-by-Step Solution:

Verification / Alternative check:We cannot deduce both category and presence in reverse; category labels alone do not imply presence.

Why Other Options Are Wrong:(ii) (iv) is possible but not a strict consequence (could as well be student). (iii) (i) is reversed order (not a logical implication).

Common Pitfalls:Reading "only" as "if and only if."

Final Answer:(i) (iii)