Chapter 9: Q5E (page 596)
To determine whether the given relation is irreflexive from the given matrix (of the relation).
The given relation is irreflexive if all the diagonal entries are \(0\).
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 directed graphs of the symmetric closures of the relations with directed graphs shown in Exercises 5-7.
Show that the relation on a non-empty set is symmetric, transitive and reflexive.
To prove that the relation \(R\) on set \(A\) is anti-symmetric, if and only if \(R \cap {R^{ - 1}}\) is a subset of the diagonal relation \(\Delta = \{ (a,a)\mid a \in A\} \)
(a) To find Relation\({R^2}\)
(b) To find Relation \({R^3}\)
(c) To find Relation \({R^4}\)
(d) To find Relation\({R^5}\)
Show that if \(R\) and \(S\) are both \(n\)-ary relations, then
\({P_{{i_1},{i_2}, \ldots ,{i_m}}}(R \cup S) = {P_{{i_1},{i_2}, \ldots ,{i_m}}}(R) \cup {P_{{i_1},{i_2}, \ldots ,{i_m}}}(S)\).
What do you think about this solution?
We value your feedback to improve our textbook solutions.
