We use the positions of the 1's in the matrix M_R to determine R (i.e., to determine the set of ordered pairs of elements of the set {a, b, c} which belong to R):

From the first row of M_R (which indicates the elements (a, x) in R, for x in A), we see that (a, a) and (a, c) are in R (but not (a, b)), because the first and third elements of the first row are the locations of the 1's.

From the second row of M_R (which indicates the elements (b, x) in R, for x in A), we see that (b, a) and (b, b) are in R (but not (b, c)), because the first and second ...

Solution Summary

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.

... (a) List the ordered pairs that belong to the relation. Keep in mind that a Hasse diagram is a graph of a partial ordering relation so it satisfies the three ...

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... Explain. If this relation is a partial order, draw its Hasse diagram. See the attachment. Ordered Pairs and Hasse Diagrams are clearly analyzed in this guide. ...

... labeled j . For instance, in the Hasse diagram of this ... Note that since any partial ordering is reﬂexive by ... R for all i. Therefore the ordered pairs that ...

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Important information about Hasse diagram. S = {0,1} and consider the partial order relation R defined on SXSXS as follows: for all ordered triples (a, b, c ...

... A by the following matrix: (see attachment for (a) Describe R by listing the ordered pairs in ... If this relation is a partial order, draw its Hasse diagram. ...

... relation a partial order, draw its Hasse diagram. ... a relation, including ordered pairs, digraphs, properties, Wasrshall's algorithm, and partial order. ...