Question-16
Consider the relation scheme \(R = (E, F, G, H, I, J, K, L, M, N)\) and the set of functional dependencies \({\{E, F\}} \rightarrow \{G\}, \{F\} \rightarrow \{I, J\}, \{E, H\} \rightarrow \{K, L\}, \{K\} \rightarrow \{M\}, \{L\} \rightarrow \{N\}\) on \(R\).
What is the key for \(R\)?
To find the key for \(R\), compute the closure of the attribute sets:
Given functional dependencies: - \(\{EF\} \rightarrow \{G\}\) - \(\{F\} \rightarrow \{I, J\}\) - \(\{EH\} \rightarrow \{K, L\}\) - \(\{K\} \rightarrow \{M\}\) - \(\{L\} \rightarrow \{N\}\)
Calculating closures: - \([\{EF\}]^+ = \{EFGIJ\}\) - \([\{E\}]^+ = \{E\}\) - \([\{EFH\}]^+ = \{EFGHIJKLMN\}\)
Since \([\{EFH\}]^+\) contains all the attributes of \(R\), \(\{EFH\}\) is the key for \(R\). Hence, the correct choice is \(\{E, F, H\}\).