\begin{frame} \frametitle{All, Any, Some} This query is equivalent to the previous query (but uses \sql{any}): \begin{code}{\textwidth}{} \small \BUseVerbatim{query2} \end{code} \pause \begin{goal}{} Note: $\{\, \sql{all}, \sql{any}, \sql{some} \,\}$ do \emph{not} extend SQL's expressiveness.\\[1ex] The statement \begin{tcenter} \sql{\underline{$A$ < any} (select \underline{$B$} from $\ldots$ where $\ldots$)} \end{tcenter} is equivalent to \begin{tcenter} \sql{\underline{exists} (select $B$ from $\ldots$ where $\ldots$ \underline{and $A$ < $B$})} \end{tcenter} \end{goal} \pause \begin{goal}{} The statement \quad \sql{$x$ in $S$} \quad is equivalent to \quad \sql{$x$ = any $S$}. \end{goal} \end{frame} \theme{Single Value Subqueries}