Explore BrainMass
Share

Explore BrainMass

    Partial order; Hasse diagram

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    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.

    © BrainMass Inc. brainmass.com October 9, 2019, 7:45 pm ad1c9bdddf
    https://brainmass.com/math/combinatorics/partial-order-hasse-diagram-128514

    Attachments

    Solution Preview

    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.

    $2.19