Chapter 9: Q3RE (page 634)
Determine an example of a relation on the set \(\{ 1,2,3,4\} \) that is Reflexive, symmetric and transitive.
The transitive relation is defined.
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Show that the relation \(R\) on a set \(A\) is antisymmetric if and only if \(R \cap {R^{ - 1}}\) is a subset of the diagonal relation \(\Delta = \{ (a,a)\mid a \in A\} \).
To prove the closure with respect to the property. ofthe relation \(R = \{ (0,0),(0,1),(1,1),(2,2)\} \) on the set \(\{ 0,1,2\} \) does not exist if . is the property" has an odd number of elements."
Let \(R\) be the relation \(\{ (a,b)\mid a \ne b\} \) on the set of integers. What is the reflexive closure of \(R\)?
Assuming that no new \(n\)-tuples are added, find a composite key with two fields containing the Airline field for the database in Table 8.
Use quantifiers to express what it means for a relation to be irreflexive.
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