Chapter 9: Q2E (page 581)
To determine the relation in tabular form, as was done in example 4.
The relation is displayed in tabular form.
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Findfor the given .
Which relations in Exercise 3 are asymmetric?
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.
To draw the Hasse diagram for divisibility on the set \(\{ 1,2,4,8,16,32,64\} \).
Exercises 34–37 deal with these relations on the set of real numbers:
\({R_1} = \left\{ {\left( {a,\;b} \right) \in {R^2}|a > b} \right\},\)the “greater than” relation,
\({R_2} = \left\{ {\left( {a,\;b} \right) \in {R^2}|a \ge b} \right\},\)the “greater than or equal to” relation,
\({R_3} = \left\{ {\left( {a,\;b} \right) \in {R^2}|a < b} \right\},\)the “less than” relation,
\({R_4} = \left\{ {\left( {a,\;b} \right) \in {R^2}|a \le b} \right\},\)the “less than or equal to” relation,
\({R_5} = \left\{ {\left( {a,\;b} \right) \in {R^2}|a = b} \right\},\)the “equal to” relation,
\({R_6} = \left\{ {\left( {a,\;b} \right) \in {R^2}|a \ne b} \right\},\)the “unequal to” relation.
36. Find
(a) \({R_1}^\circ {R_1}\).
(b) \({R_1}^\circ {R_2}\).
(c) \({R_1}^\circ {R_3}\).
(d) \({R_1}^\circ {R_4}\).
(e) \({R_1}^\circ {R_5}\).
(f) \({R_1}^\circ {R_6}\).
(g) \({R_2}^\circ {R_3}\).
(h) \({R_3}^\circ {R_3}\).
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