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Key to exercises.

Today I saw the quoted sentence when looking at the keys to exercises, and afterwards that sentence got me thinking why the preposition to is used here instead of for.

The way I see it is that the key purpose is to match our answer with the correct one; hence, for would fit here nicely. Am I right?

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    Because keys in the standard sense go to locks. Commented Aug 9, 2012 at 20:33
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    I've heard them used interchangeably, so the answer might well be subtle or paved over by misuse.
    – rsegal
    Commented Aug 9, 2012 at 20:50
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    If I'm understanding this question correctly, I would simply use the term "Answer Key" and avoid the preposition altogether.
    – J.R.
    Commented Aug 9, 2012 at 20:56
  • I suspect there is a similar principle in effect when stating "the answer to your question is" versus "the answer for your question is", but I don't know if this is indicative of some English rule or just a "fact" of general usage. It reminds me of the difference between por and para in Spanish, though.
    – Zairja
    Commented Aug 9, 2012 at 21:02
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    "Key to" if far more common, despite "key of" being used for music (e.g., "in the key of C").
    – jimm101
    Commented Feb 6, 2022 at 17:15

2 Answers 2

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As I stated in comment, keys in the standard sense pair with locks. Copies can be made, but in theory, each lock has only one key that unlocks it. See also:

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    I'd go for the same expression you indicate, that is "key to"; however, the OP indicated "for" as the preposition of his choice, so your last sentence is not entirely suitable.
    – Paola
    Commented Aug 9, 2012 at 21:44
  • "Do you have the key for the back door?": Perfectly normal idiomatic English.
    – phoog
    Commented Feb 23 at 11:05
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I can see using “key to” when the “to” is part of a verb phrase. “The key to unlock the door is under the mat.” “The key to understanding the problem was remembering PEMDAS.”

If a preposition and a linking verb are used, perhaps “for” is a better choice. "To stay healthy, the key for me is watching my weight."

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    In "the key to understanding the problem", the part after to is a noun phrase, not a verb phrase. To is a preposition there. In "the key to unlock the door", to is part of the infinitive; of course you can call it a verb phrase if you must, but that's unnecessarily misleading. It looks like you opted for the term only to have a convenient (but wrong) hypernym.
    – RegDwigнt
    Commented Nov 15, 2012 at 19:45
  • @RegDwigнt is it really part of the infinitive or is it a preposition expressing the purpose of the key or the instrumental relationship between the key and the door? Or is that function of the preposition the thing that led to our considering "to" as part of the infinitive, unlike more inflected languages ?
    – phoog
    Commented Feb 23 at 11:11

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