Chapter 9: Q3E (page 589)
List the 5 -tuples in the relation in Table 8.
The resultant answer is explained.
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To determine an example of an irreflexive relation on the set of all people.
Let \(R\) be the relation \(\{ (a,b)\mid a \ne b\} \) on the set of integers. What is the reflexive closure of \(R\)?
To determine whether the relationon the set of all people is reflexive, symmetric, anti symmetric, transitive, where if and only if aand have a common grandparent.
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.
35. Find
(a) \({R_2} \cup {R_4}\).
(b) \({R_3} \cup {R_6}\).
(c) \({R_3} \cap {R_6}\).
(d) \({R_4} \cap {R_6}\).
(e) \({R_3} - {R_6}\).
(f) \({R_6} - {R_3}\).
(g) \({R_2} \oplus {R_6}\).
(h) \({R_3} \oplus {R_5}\).
How many different relations are there from a set with elements to a set with elements?
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