Chapter 9: Q62E (page 618)
Determine the number of different equivalence relations on a set with four elements by listing them.
There are \(15\) distinct equivalence relations on \(S\), as listed below.
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Which relations in Exercise 5 are irreflexive?
To prove that the relation \(R\) on a set \(A\) is symmetric if and only if \(R = {R^{ - 1}}\) where \({R^{ - 1}}\) is the inverse relation.
(a) To find Relation \({R_1} \cup {R_2}\).
(b) To find Relation \({R_1} \cap {R_2}\).
(c) To find Relation \({R_1} - {R_2}\).
(d) To find Relation \({R_2} - {R_1}\).
(e) To find Relation \({R_1} \oplus {R_2}\).
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.
To determine whether the relation R on the set of all web pages is reflexive, symmetric, anti symmetric, transitive, where if and only if there is a webpage that includes links to both webpage a and webpage b.
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