Question
Compute the closure of the following set F of functional dependencies for relation schema
R = (A, B, C, D, E).
List the candidate keys for R.
Answer :
Word Count : 647
We are given: Relation Schema: $R(A, B, C, D, E)$ Functional Dependencies (FDs): 1. $A \rightarrow BC$ 2. $CD \rightarrow E$ 3. $B \rightarrow D$ 4. $E \rightarrow A$ We are to compute $F^+$ (closure of F) and list candidate keys. --- ### Step 1: Compute the attribute closures to find candidate keys The candidate key is an attribute set whose closure gives all attributes $\{A, B, C, D, E\}$. Let’s check single attribute closures first: --- #### (i) $A^+$ Start with $\{A\}$: 1. $A \rightarrow BC$ ⇒ $\{A, B, C\}$ 2. $B \rightarrow D$ ⇒ $\{A, B, C, D\}$ 3. $CD \rightarrow E$ ⇒ $\{A, B, ____ _______ __________ _____ _____ _____ _________ _____ _________ _________.
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We are given: Relation Schema: $R(A, B, C, D, E)$ Functional Dependencies (FDs): 1. $A \rightarrow BC$ 2. $CD \rightarrow E$ 3. $B \rightarrow D$ 4. $E \rightarrow A$ We are to compute $F^+$ (closure of F) and list candidate keys. --- ### Step 1: Compute the attribute closures to find candidate keys The candidate key is an attribute set whose closure gives all attributes $\{A, B, C, D, E\}$. Let’s check single attribute closures first: --- #### (i) $A^+$ Start with $\{A\}$: 1. $A \rightarrow BC$ ⇒ $\{A, B, C\}$ 2. $B \rightarrow D$ ⇒ $\{A, B, C, D\}$ 3. $CD \rightarrow E$ ⇒ $\{A, B, ____ _______ __________ _____ _____ _____ _________ _____ _________ _________.
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