Chapter 9: Q47E (page 617)
To determine the list of ordered pairs in the equivalence relations produced by these partitions of \(\{ 0,1,2,3,4,5\} \).
The list of ordered pair is \(R = \{ (0,0),(1,1),(2,2),(3,3),(4,4),(5,5)\} \).
Over 22 million students worldwide already upgrade their learning with Vaia!
All the tools & learning materials you need for study success - in one app.
Get started for free
Find the error in the "proof" of the following "theorem."
"Theorem": Let \(R\) be a relation on a set \(A\) that is symmetric and transitive. Then \(R\) is reflexive.
"Proof": Let \(a \in A\). Take an element \(b \in A\) such that \((a,b) \in R\). Because \(R\) is symmetric, we also have \((b,a) \in R\). Now using the transitive property, we can conclude that \((a,a) \in R\) because \((a,b) \in R\)and \((b,a) \in R\).
Which relations in Exercise 4 are irreflexive?
Draw the Hasse diagram for the less than or equal to relation on \(\{ 0,2,5,10,11,15\} \).
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.
To determine the relation in tabular form, as was done in example 4.
What do you think about this solution?
We value your feedback to improve our textbook solutions.
