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Exercise 73 - Chapter 3

Note that \( \mathcal{G} \) is isomorphic to the schema \( \textbf{Gr} \). In Section 3.3.5 we saw that instances on \( \textbf{Gr} \) are graphs. Draw the sample instance \(I\) as a graph.

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The sample instance \( I : \mathcal{G} \rightarrow \textbf{Set} \). $$ \begin{matrix} \begin{array}{c | c c } \text{Email} & \text{sent_by} & \text{received_by} \\\\ \hline \text{Em_1} & \tt{Bob} & \tt{Grace} \\\\ \text{Em_2} & \tt{Grace} & \tt{Pat} \\\\ \text{Em_3} & \tt{Bob} & \tt{Emory} \\\\ \text{Em_4} & \tt{Sue} & \tt{Doug} \\\\ \text{Em_5} & \tt{Doug} & \tt{Sue} \\\\ \text{Em_6} & \tt{Bob} & \tt{Bob} \end{array} & \begin{array}{c | } \tt{Address} \\\\ \hline \tt{Bob} \\\\ \tt{Doug} \\\\ \tt{Emory} \\\\ \tt{Grace} \\\\ \tt{Pat} \\\\ \tt{Sue} \end{array} \end{matrix} $$

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  • 1.

    \(\require{AMScd}\) \begin{CD} \text{EM}_6\unicode{10227}\tt{Bob} @>\text{EM}_1>> \tt{Grace} \\@V\text{EM}_3VV {}@VV\text{EM}_2V \\ \tt{Emory} @. \tt{Pat} \end{CD} \begin{array}{ccc} \tt{Sue}&\unicode{8644}_{\text{EM}_5}^{\text{EM}_4}&\tt{Doug} \end{array}

    Comment Source:\\(\require{AMScd}\\) \begin{CD} \text{EM}\_6\unicode{10227}\tt{Bob} @>\text{EM}\_1>> \tt{Grace} \\\@V\text{EM}\_3VV {}@VV\text{EM}\_2V \\\ \tt{Emory} @. \tt{Pat} \end{CD} \begin{array}{ccc} \tt{Sue}&\unicode{8644}\_{\text{EM}\_5}^{\text{EM}\_4}&\tt{Doug} \end{array}
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