\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}