\frametitle{Implication of Functional Dependencies}

  Compute the cover $\{\sql{ISBN}\}^+$ for the following FDs:
    \sql{ISBN}           & \to \sql{TITLE}, \sql{PUBLISHER} \\
    \sql{ISBN}, \sql{NO} & \to \sql{AUTHOR} \\
    \sql{PUBLISHER}      & \to \sql{PUB\_URL} 
  \item We start with $x = \{\sql{ISBN}\}$.
  \item The FD $\sql{ISBN} \to \sql{TITLE}, \sql{PUBLISHER}$ is applicable
    since the left-hand side of is completely contained in $x$.
    We get $x = \{ \sql{ISBN}, \sql{TITLE}, \sql{PUBLISHER} \}$.
  \item Now the FD $\sql{PUBLISHER} \to \sql{PUB\_URL}$ is applicable.\\
    We get $x = \{\sql{ISBN}, \sql{TITLE}, \sql{PUBLISHER}, \sql{PUB\_URL}\}$.
  \item No further way to extend set $x$, the algorithm returns
      \{\sql{ISBN}\}^+ = \{\sql{ISBN}, \sql{TITLE}, \sql{PUBLISHER}, \sql{PUB\_URL}\}
  \item \pause We may now conclude, e.g., $\sql{ISBN} \to \sql{PUB\_URL}$.