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Since candidate key is a minimal key and it is a proper subset of a super-key , then how is it that for a candidate key ,its proper subset is not a super key ?
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A candidate key is the minimal superkey. That means if we try to remove some attributes from the candidate key (minimal super key) we will no more get a superkey as it was the minimal. Hence, any proper subset of the candidate key is not a superkey.

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