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Sierra goes for a walk if and only if Columbine goes for a walk.

A) Sierra and Columbine always go for a walk together.
B) Sierra and Columbine never go for a walk together.
C) Sierra goes for a walk only if Columbine does.
D) Columbine goes for a walk only if Sierra does.

1 Answer

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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.

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