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GATE Overflow Test Series | Databases | Test 1 | Question: 23

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Mark all the correct statements given below
  1. Number of super keys of any relation cannot be more than twice the number of candidate keys
  2. The candidate key with the smallest number of attributes is chosen as the primary key
  3. A prime attribute must be part of all the candidate keys
  4. A prime attribute must be part of some candidate key
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Option A is false. Consider a relation with $3$ attributes where only one is the candidate key. By choosing from any subset of the remaining $2$ attributes including empty set we get $2^2 = 4$ super keys.

Option B is false as any of the candidate key can be chosen as the primary key without any special requirement.

By definition a prime attribute is any attribute part of "some" candidate key. So, option C is false and D is true.

Correct option: D.
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