\begin{frame}
  \frametitle{Third Normal Form}

  \begin{block}{}
    A \emph{key attribute} is an attribute that
    appears in a minimal key.\\
    \remark{Minimality is important, otherwise all attributes are key attributes.}
  \end{block}
  \smallskip
  \pause
  
  \textit{{\small Assume that every FD has a single attribute on the right-hand side.\\
  If not, expand FDs with multiple attributes on the right-hand side.}}
  \pause
  \begin{block}{Third Normal Form (3NF)}
  A relation $R$ is in \emph{Third Normal Form (3NF)} if and only if
  every FD $A_1, \dots, A_n \to B$
  satisfies at least one of the conditions:
  \pause
  \begin{itemize}
    \item $\{\, A_1, \dots, A_n \,\}$ contains a key of $R$, or
    \item the FD is trivial (that is, $B \in \{\, A_1, \dots, A_n \,\}$), or
    \pause
    \item \alert{$B$ is a \emph{key attribute} of $R$.}
  \end{itemize}
  \end{block}
  \remark{The only difference with BCNF is the last condition.}
  \smallskip
  \pause
  
  \begin{goal}{}
    Third Normal Form (3NF) is slightly weaker than BCNF:\\
    If a relation is in BCNF, it is automatically in 3NF.
  \end{goal}
  % In some rare scenarios, 
  % a relation cannot be transformed to BCNF while preserving all FDs.
  % With 3NF the transformation is always possible.
\end{frame}