Chapter 9: Q16E (page 597)
To calculate the number of non-zero entries in the matrix \({M_{{R^{ - 1}}}}\).
The number of non-zero entries of \({M_{{R^{ - 1}}}}\) is also \(k\).
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To find the smallest relation of the relation \(\{ (1,2),(1,4),(3,3),(4,1)\} \) which is reflexive, symmetric and transitive.
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.
List the 5 -tuples in the relation in Table 8.
In Exercises 25–27 list all ordered pairs in the partial ordering with the accompanying Hasse diagram.
26.
Find all circuits of length three in the directed graph in Exercise 16.
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