Chapter 9: Q2RE (page 634)
What is a transitive relation?
The transitive relation is defined.
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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.
Use quantifiers to express what it means for a relation to be asymmetric.
Findfor the given .
To determine for each of these relations on the set decide whether it is reflexive, whether it is symmetric, whether it is anti symmetric, and whether it is transitive .
Whether there is a path in the directed graph in Exercise 16 beginning at the first vertex given and ending at the second vertex given.
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