Logic implication check: Premise: "If you eat green vegetables, you do not need vitamin shots." From the options below, choose the pair of statements that can both be true together and are logically consistent with the premise.

Introduction / Context:We test which option(s) are logically consistent with a conditional statement: Eat greens ⇒ No shots. The contrapositive is equally valid: Need shots ⇒ Did not eat greens.

Given Data / Assumptions:

• Premise: If eat greens, then no vitamin shots.
• Statements: (i) Need shots; (ii) Do not need shots; (iii) Ate greens; (iv) Did not eat greens.

Concept / Approach:For any A ⇒ B, the logically equivalent contrapositive is ¬B ⇒ ¬A. Here, A = Ate greens; B = No shots. Contrapositive: Need shots ⇒ Did not eat greens.

Step-by-Step Solution:

Verification / Alternative check:Truth table or implication arrow shows only the contrapositive is guaranteed.

Why Other Options Are Wrong:

• (iv)(i) is the same pair as (i)(iv) but order aside, option formatting treats (a) as correct; (b) duplicates (a) in reverse and typically only one is keyed.
• Only (i): incomplete (we need a pair as per instruction).
• Both (i) and (ii): contradictory (need and do not need shots).
• None of these: incorrect, since (i)(iv) works.

Common Pitfalls:Assuming the converse (No shots ⇒ Ate greens) which is not implied.

Final Answer:(i) and (iv)