\begin{frame}
  \frametitle{Database States: Tuples}

   \vspace*{-.4ex}  
  \begin{goal}{}
  Tuples are used to formalise table rows.
  \end{goal}

  \begin{block}{}
    A \textbf{tuple} $t$ with respect to the relation schema
    \begin{talign}
    s = (A_1:D_1, \dots, A_n:D_n)
    \end{talign}
    is a sequence $t = (d_1, \dots, d_n)$ of values such that $d_i \in \dom{D_i}$.
  \end{block}
  In other words: $t \in \dom{D_1} \times \cdots \times \dom{D_n}$.
   
  \begin{exampleblock}{}
    For instance, $(\sql{\textquotesingle{}exam\textquotesingle{}}, \sql{1}, \sql{\textquotesingle{}SQL\textquotesingle{}},\sql{14})$ is a tuple in the table \vspace{-1ex}
    \begin{center}
    {\ttfamily\footnotesize\tableExercises}
    \end{center}
  \end{exampleblock}
  \pause\smallskip
  
  \begin{block}{}
    Given a tuple $t$, we write $t.A_i$ for the value in column $A_i$.
  \end{block}
  \begin{exampleblock}{}
    For instance, 
    $(\sql{\textquotesingle{}exam\textquotesingle{}}, \sql{1}, \sql{\textquotesingle{}SQL\textquotesingle{}},\sql{14}).\sql{topic} = \sql{\textquotesingle{}SQL\textquotesingle{}}$.
  \end{exampleblock}
  \vspace{10cm}
\end{frame}