Chapter 9: Q65E (page 618)
To determine the partition \(Q\) arising from equivalence relation \(R\) corresponding to a given partition \(P\).
$Q$ and $P$ define the same partitions.
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Suppose that \(R\) and \(S\) are reflexive relations on a set \(A\).
Prove or disprove each of these statements.
a) \(R \cup S\) is reflexive.
b) \(R \cap S\) is reflexive.
c) \(R \oplus S\) is irreflexive.
d) \(R - S\) is irreflexive.
e) \(S^\circ R\) is reflexive.
To prove that the relation \(R\) on set \(A\) is anti-symmetric, if and only if \(R \cap {R^{ - 1}}\) is a subset of the diagonal relation \(\Delta = \{ (a,a)\mid a \in A\} \)
What do you obtain when you apply the selection operator \({s_C}\), where \(C\) is the condition (Airline = Nadir) \( \vee \) (Destination = Denver), to the database in Table 8?
Draw the Hasse diagram for the greater than or equal to relation on \(\{ 0,1,2,3,4,5\} \).
In Exercises 25–27 list all ordered pairs in the partial ordering with the accompanying Hasse diagram.
25.
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