Consider a relational database schema with a relation $R(A, B, C, D)$. If $\{A, B\}$ and $\{A, C\}$ are the only two candidate keys of the relation $R$, then the number of superkeys of relation $R$ is ________. (answer in integer)

A superkey is any superset of a candidate key.

The relation has 4 attributes: $U = \{A, B, C, D\}$. The given candidate keys are $K_1 = \{A, B\}$ and $K_2 = \{A, C\}$.

1. Supersets containing $K_1 = \{A, B\}$: The remaining attributes are $\{C, D\}$ (2 attributes).

   $$\text{Number of superkeys containing } \{A, B\} = 2^2 = 4$$

   These are: $\{A, B\}, \{A, B, C\}, \{A, B, D\}, \{A, B, C, D\}$.

2. Supersets containing $K_2 = \{A, C\}$: The remaining attributes are $\{B, D\}$ (2 attributes).

   $$\text{Number of superkeys containing } \{A, C\} = 2^2 = 4$$

   These are: $\{A, C\}, \{A, B, C\}, \{A, C, D\}, \{A, B, C, D\}$.

3. Supersets containing both $\{A, B\}$ and $\{A, C\}$, i.e., containing $\{A, B, C\}$: The remaining attribute is $\{D\}$ (1 attribute).

   $$\text{Number of superkeys containing both } = 2^1 = 2$$

   These are: $\{A, B, C\}, \{A, B, C, D\}$.

By the Principle of Inclusion-Exclusion: