Question

[5] (5%) it is known that for r(a,b,c,d,e): 1. r has exactly two candidate keys 2. a is a candidate key. 3. d and e are non-prime attributes. how many superkeys can r have?

Answer 1

The number of superkeys that relation r(a,b,c,d,e) can have is infinite.

Step-by-step explanation:

In this case, the relation r(a,b,c,d,e) has exactly two candidate keys, with a being one of them. Additionally, d and e are non-prime attributes. To determine the number of superkeys, we need to consider that a superkey is a set of attributes that can uniquely identify a tuple in a relation. Since a candidate key is a minimal superkey, we can add any attributes to it and still have a superkey.

Since we know that a is a candidate key, any superkey must contain a as one of its attributes. We also know that d and e are non-prime attributes, which means they are not part of any candidate key. Therefore, we can add d and e to any candidate key to create a superkey.

Therefore, the number of superkeys that relation r(a,b,c,d,e) can have is infinite, as we can add any combination of attributes to the candidate key a to create a superkey.