Let A = {a, b, c} , and let R be the relation defined on A defined by
the following matrix:
Which of the properties: reflexive, antisymmetric and transitive are
true for the given relation?
Begin your discussion by defining each term in general first and then
how the definition relates to this specific example.
Mathematics Homework Solutions
#127237
A binary relation R is defined in terms of a given matrix. Define what it means for a relation to be (a) reflexive, (b), antisymmetric, and (c) transitive. Also, determine which of these are properties of R.
For the set A = {a, b, c}, let R be the relation on A which is defined by the following 3 by 3 matrix M_R:
----------------------------------------
Row 1: 1 0 1
Row 2: 1 1 0
Row 3: 0 1 1
-----------------------------------------
Which of the properties (reflexive, antisymmetric, transitive) are satisfied by R?
Begin your discussion by defining each property in general, and then determine whether R satisfies that property.
Definitions are given of the following properties of a binary relation: reflexive, antisymmetric, and transitive. A detailed determination of which of these are properties of the given relation is presented.
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