Final answer:
In Mathematics, the statement 'Sierra goes for a walk if and only if Columbine goes for a walk' implies a biconditional relationship, which means both Sierra and Columbine either go for a walk together (Option A) or do not go at all, and Sierra will only walk if Columbine does (Option C).
Step-by-step explanation:
The question involves understanding logical statements and their implications in a given scenario, which is a topic covered within Mathematics, particularly in the area of logic. The indicative phrase 'if and only if' specifies a biconditional logical relationship between the actions of Sierra and Columbine. The correct answer to the question is provided by options A and C. This is because 'Sierra goes for a walk if and only if Columbine goes for a walk' states that both events must occur together or not at all, hence they always go for a walk together and Sierra walks only if Columbine walks.
Option B is incorrect because it states that they never go for a walk together, which contradicts the 'if and only if' condition. Option D might seem correct, but it's not necessarily true given the statement made, because it's the condition of Columbine going for a walk that is necessary for Sierra to walk, not the other way around; D is merely the converse of C and the statement doesn't assert this converse.