Consider relation R(A,B,C,D,E) with functional dependencies:AB -> C, C -> D, BD -> EWhich of the following sets of attributes does not functionally determine E

To determine which set of attributes does not functionally determine $E$ in relation $R(A,B,C,D,E)$ given the functional dependencies $AB \rightarrow C$, $C \rightarrow D$, and $BD \rightarrow E$, we'll analyze the sets of attributes based on the provided functional dependencies.

Step 1: Understand Functional Dependencies

• $AB \rightarrow C$: Knowing $A$ and $B$ allows us to determine $C$.
• $C \rightarrow D$: Knowing $C$ allows us to determine $D$.
• $BD \rightarrow E$: Knowing $B$ and $D$ allows us to determine $E$.

Step 2: Analyze Each Set of Attributes

We need to evaluate which specific set does not lead to the determination of $E$.

1. Set: {A, B}

   • From $AB \rightarrow C$, we can determine $C$.
   • Then, from $C \rightarrow D$, we can determine $D$.
   • Finally, using $B$ and $D$, we can determine $E$.
   • Determines $E$.

2. Set: {B, C}

   • From $B$ and $C$, we can directly determine $D$ from $C \rightarrow D$.
   • Using $B$ and $D$, we can determine $E$.
   • Determines $E$.

3. Set: {C, D}

   • From $C$, we can determine $D$ (no new information).
   • We can't determine $B$ directly, and $B$ is essential to determine $E$ using the dependency $BD \rightarrow E$.
   • Does not determine $E$.

4. Set: {B, D}

   • Using $B$ and $D$, we can determine $E$ directly.
   • Determines $E$.

Step 3: Conclusion

The set of attributes that does not functionally determine $E$ is:

$\text{Set: } \{C, D\}$

Final Answer

The set of attributes that does not functionally determine $E$ is {C, D}.