Chapter 9: Q5E (page 596)
To determine whether the given relation is irreflexive from the given matrix (of the relation).
The given relation is irreflexive if all the diagonal entries are \(0\).
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Adapt Algorithm 1 to find the reflexive closure of the transitive closure of a relation on a set with \(n\) elements.
Findfor the given .
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.
Which of these relations on \(\{ 0,1,2,3\} \) are equivalence relations? Determine the properties of an equivalence relation that the others lack.
Which relations in Exercise 4 are asymmetric?
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