The relation R(A,B,C,D,E,F) with functional dependency set F = {AB -> CD, C -> CA, B -> E, D -> B, E -> F}The number of candidate keys of a relation R is ______.

To find the candidate keys of a relation R, we need to follow these steps:

1. Identify the attributes that do not appear on the right side of any functional dependency. These attributes will definitely be a part of every candidate key. In this case, these attributes are A and C.

2. Now, we need to find the closure of these attributes. The closure of an attribute set is the set of all attributes that can be functionally determined by that attribute set.

   Let's find the closure of {A, C}:

   • Start with {A, C}
   • AB -> CD, but we don't have B, so we can't use this rule.
   • C -> CA, but we already have A and C, so this rule doesn't add anything.
   • B -> E, but we don't have B, so we can't use this rule.
   • D -> B, but we don't have D, so we can't use this rule.
   • E -> F, but we don't have E, so we can't use this rule.

   So, the closure of {A, C} is {A, C} itself.

3. If the closure of an attribute set includes all attributes of the relation, then that attribute set is a candidate key. In this case, {A, C} does not include all attributes of the relation (it's missing B, D, E, and F), so it's not a candidate key.

4. If the closure of an attribute set does not include all attributes, then we need to add more attributes to the set and find the closure again. We add those attributes that are on the left side of a functional dependency and not included in the closure yet.

   Let's add B to the set and find the closure of {A, B, C}:

   • Start with {A, B, C}
   • AB -> CD, so we can add D to the set. Now the set is {A, B, C, D}
   • C -> CA, but we already have A and C, so this rule doesn't add anything.
   • B -> E, so we can add E to the set. Now the set is {A, B, C, D, E}
   • D -> B, but we already have B, so this rule doesn't add anything.
   • E -> F, so we can add F to the set. Now the set is {A, B, C, D, E, F}

   So, the closure of {A, B, C} is {A, B, C, D, E, F}, which includes all attributes of the relation.

5. Therefore, {A, B, C} is a candidate key.

6. We need to check if there are any other candidate keys. To do this, we need to check if there are any proper subsets of {A, B, C} whose closure includes all attributes of the relation. In this case, there are no such subsets.

So, the number of candidate keys of the relation R is 1, and the candidate key is {A, B, C}.