6.6

Consider the representation of the ternary relationship of Figure 6.29a using the binary relationships illustrated in Figure 6.29b (attributes not shown).

  1. Show a simple instance of \(E\),\(A\),\(B\),\(C\),\(R_A\),\(R_B\), and \(R_C\) that cannot correspond to any instance of \(A\), \(B\), \(C\), and \(R\).

  2. Modify the E-R diagram of Figure 6.29b to introduce constraints that will guarantee that any instance of \(E\),\(A\),\(B\),\(C\),\(R_A\),\(R_B\), and \(R_C\) that satisfies the constraints will correspond to an instance of \(A\), \(B\), \(C\), and \(R\).

  3. Modify the preceding translation to handle total participation constraints on the ternary relationship.

  1. Let \(E = \{e_1, e_2\}\), \(A = \{a_1, a_2\}\), \(B = \{b_1\}\), \(C = \{c_1\}\), \(R_A = \{ (e_1, a_1), (e_2, a_2)\}\), \(R_B = \{ (e_1, b_1)\}\), \(R_C = \{ (e_1, c_1)\}\). We see that because of the tuple \((e_2,a_2)\), no instance of \(A\),\(B\),\(C\), and \(R\) exists that correspond to \(E\),\(R_A\),\(R_B\), and \(R_C\)

  2. See Figure 6.105. The idea is to introduce total participation constraints between \(E\) and the relationships \(R_A\), \(R_B\), \(R_C\) so that every tuple in \(E\) has a relationship with \(A\),\(B\), and \(C\).

  1. Suppose \(A\) totally participates in the relationship \(R\), then introduce a total participation constraint between \(A\) and \(R_A\), and similarly for \(B\) and \(C\).