\begin{frame}
  \frametitle{Boyce-Codd Normal Form: Quiz}

  \begin{quiz}{\textwidth}{BCNF Quiz}
    {\small
    \begin{enumerate}
    \item
      Consider the relation
      \begin{tcenter}
        \vspace{-.25ex}
        \sql{Results(sid, exercise, points, maxPoints)}
        \vspace{-.25ex}
      \end{tcenter}
      with the following FDs 
      \begin{tcenter}
        $
        \begin{array}{rcl}
          \sql{sid, exercise} & \to & \sql{points} \\
          \sql{exercise}           & \to & \sql{maxPoints}
        \end{array}
        $
      \end{tcenter}
      Is this relation in BCNF?
    \pause
    
    \item
      Consider the relation
      \vspace{-.5ex}
      \begin{talign}
        \sql{Invoice(} & \sql{invoiceNr, date, amount,} \\[-.5ex]
                       & \sql{customerNr, customerName)}
      \end{talign}
      \vspace{-.5ex}
      with the following FDs 
      \begin{tcenter}
        $
        \begin{array}{rcl}
          \sql{invoiceNr} & \to & \sql{date}, \sql{amount}, \sql{customerNr}
          \\
          \sql{invoiceNr}, \sql{date} & \to & \sql{customerName} 
          \\
          \sql{customerNr} & \to & \sql{customerName}
          \\
          \sql{date}, \sql{amount} & \to & \sql{date} 
        \end{array}
        $
      \end{tcenter}      
      Is this relation in in BCNF?
    \end{enumerate}
    }
  \end{quiz}  

  %% (1)
  %% -- STUD_ID, EX_NO is key of RESULTS
  %% => first FD implied by key (lhs is key)
  %% => second FD not implied by key (lhs does not contain key)
  %% => not in BCNF (embedded function EX_NO -> MAX_POINTS)
  %%
  %% (2)
  %% -- INV_NO is key of INVOICE (first FD + third FD and transitivity)
  %% => first FD implied by key (lhs is key)
  %% => second FD implied by key (lhs contains key)
  %% => third FD not implied by key 
  %% => fourth FD trivial (to be ignored)
  %% => not in BCNF (embedded function CUST_NO -> CUST_NAME)
\end{frame}

\theme{Third Normal Form}