Jacob Wilkins (1/11/2016)

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I understand your reasoning, but that's not the correct scope for the OR in that English construction.

The construction "X, whether Y or not-Y", is equivalent to "IF (y OR not-Y), THEN X". It is not[/i] equivalent to "(IF y THEN x) OR (IF not-y THEN x)". Put in those formal logic symbols we all love so much, it is the first of the following two:

(Y ? ¬Y)?X This correctly represents the English "X, whether Y or not-Y"

(Y?X) ? (¬Y?X) This is an incorrect representation of the English "X, whether Y or not-Y"

That first is actually just equivalent to X, which is not surprising, because that English construction is used to emphasize that the truth value of Y is irrelevant to the truth value of X.

That means that the answer "Dropping an index on the table invalidates the plan, whether the index is used by the plan or not", is equivalent to "Dropping an index on the table invalidates the plan", which is indeed incorrect.

Hopefully that helps clear up the confusion about the wording, and doesn't just muddy the waters 🙂

Cheers!