Chapter 9: Q64E (page 618)
Do we necessarily get an equivalence relation when we form the symmetric closure of the reflexive closure of the transitive closure of a relation?
It is true that the symmetric closure of the reflexive closure of the transitive closure of a relation is an equivalence relation.
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To determine whether the relation on the set of all real numbers is reflexive, symmetric, anti symmetric, transitive, where if and only ifx=1 or y=1.
To find the ordered pairs in \({R^3}\) relation.
What do you obtain when you apply the selection operator \({s_C}\), where \(C\) is the condition Destination = Detroit, to the database in Table 8?
Let \(A\) be the set of students at your school and \(B\) the set of books in the school library. Let \({R_1}\) and \({R_2}\) be the relations consisting of all ordered pairs \((a,b)\), where student \(a\) is required to read book \(b\) in a course, and where student \(a\) has read book \(b\), respectively. Describe the ordered pairs in each of these relations.
a) \({R_1} \cup {R_2}\)
b) \({R_1} \cap {R_2}\)
c) \({R_1} \oplus {R_2}\)
d) \({R_1} - {R_2}\)
e) \({R_2} - {R_1}\)
Determine whether the relation R on the set of all real numbers are asymmetric.
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