Math 213, Quiz 8 (Solutions); Friday, March 28, 2008
1. Let A={1,2,3}and let
R={(1,1),(2,2),(3,3),(1,2),(2,3),(2,1),(3,2)}
be a relation on A.
(a) Is the relation R
(1) reflexive?
(2) symmetric?
(3) transitive?
Provide explanation of your answers.
(b) Write down the matrix MRrepresenting this relation.
Solution.
(a)
(1) Relation Ris reflexive since (1,1),(2,2),(3,3) ∈R.
(2) Yes, the relation is symmetric.
(3) No, the relation is not transitive. Indeed, (1,2),(2,3) ∈Rbut
(1,3) 6∈ R.
(b)
MR=
110
111
011
.
1