Conditional "only when": Premise: "He works at the farm only when his father asks him politely." Which pair of statements can both be true and is logically required by the premise?

Introduction / Context:"Only when" expresses a necessary condition. "He works at the farm only when his father asks him politely" means: If he worked at the farm, then his father must have asked politely.

Given Data / Assumptions:

• Premise: Work-at-farm ⇒ Father-asked-politely.
• Statements: (i) He worked at the farm. (ii) Father asked politely. (iii) He worked at home. (iv) Father did not ask politely.

Concept / Approach:For A only when B, we formalize as A ⇒ B. The contrapositive is ¬B ⇒ ¬A. The premise does not guarantee the converse B ⇒ A.

Step-by-Step Solution:

Verification / Alternative check:The pair (i) & (ii) exactly matches A ⇒ B becoming true with A observed; hence it is required.

Why Other Options Are Wrong:

• (ii) with (i) reordered is equivalent, but the key selects one canonical ordering.
• (iii) with (iv) or (ii) says nothing about the farm condition and doesn’t satisfy the necessity relation explicitly.
• None of these is wrong because a correct pair exists.

Common Pitfalls:Interpreting "only when" as "if and only if"; the premise does not assert the converse.

Final Answer:(i) and (ii)