Final answer:
The candidate keys for the schema R, considering the given functional dependencies, are IJ and DE. These are determined via the process of elimination and ensuring the definition of a candidate key as the minimal set of attributes that determines all other attributes in the schema.
Step-by-step explanation:
The student's question pertains to finding all candidate keys for a given schema R with various functional dependencies. The schema R is represented as (A, B, C, D, E, G, H, I, J, K) and the functional dependencies are A → B, DE → GHI, EG → AB, JC → B, IJ → CD, and J → E.
To identify the candidate keys, we must find the minimal set of attributes that can uniquely identify a tuple in the relation. We first examine the given dependencies to determine which attributes are generated by others and those that are not. Since J generates E and C generates B, we can eliminate B and E from the key consideration. Next, we see that DE generates GHI, and EG generates A and JC. As such, J is also not necessary for the key because it can be generated from other attributes.
After examining all the dependencies, we determine that the attributes D, I, and perhaps C are necessary to generate all other attributes, making DIC a potential candidate key. However, since IJ generates CD, we can also have IJ as the minimal generating set, ruling out C. In conclusion, IJ and DE are potential candidate keys. To ensure these are the only candidate keys, we have shown that all attributes of R can be generated from these sets and there are no smaller sets that can generate R, which fulfills the definition of a candidate key.