Let A = {a, b, c} , and let R be the relation defined on A defined by
the following matrix:
(a) Describe R by listing the ordered pairs in R and draw the digraph
of this relation.
(b) 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.
(c) Is this relation a partial order? Explain. If this relation a
partial order, draw its Hasse diagram.
(d) Use Warshall’s Algorithm to determine the transitive closure of
R. Note there are 2 versions of Washall’s Algorithm traditionally
given. Use any version you wish.
Draw the digraph of the transitive closure of R and use the digraph to
explain the idea of connectivity. Is this graph connected? What does
connectivity mean?
Mathematics Homework Solutions
#128514
A binary relation R is defined in terms of a given matrix. Determine whether R is a partial order. If it is, draw its Hasse diagram.
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
-----------------------------------------
Determine whether R is a partial order. If it is, draw its Hasse diagram.
A detailed determination of whether the given binary relation is a partial order is presented. If it is a partial order, its Hasse diagram is also drawn.
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