Explore BrainMass

Explore BrainMass

    Discrete Math: Binary Relations

    Not what you're looking for? Search our solutions OR ask your own Custom question.

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

    Please see the attached file for the fully formatted problems.

    SECTION 10.2

    For #2: A binary relation is defined on the set A = {0, 1, 2, 3}. For the relation given,
    a. draw the directed graph (See drawing tips in the Overview)
    b. determine whether the relation is reflexive
    c. determine whether the relation is symmetric
    d. determine whether the relation is transitive
    Give a counterexample in each case in which the relation does not satisfy one of the properties.

    2. R2 = {(0,0), (0, 1), (1, 1), (1, 2), (2, 2), (2, 3)}

    16. Determine whether or not the given binary relation is reflexive, symmetric, transitive, or none of these. Justify your answers.
    F is the congruence modulo 5 relation on Z: for all m, n  Z, m F n  5 | (m - n).
    Hint: Model your work on the examples in the Important Points discussion of section 10.2 or on Example 10.2.5 on pages 552-553. [When justifying your answer for each property, either include a discussion OR a formalized proof. It is not required to do both a discussion and a proof, as the textbook does in its example.]

    24. Determine whether or not the given binary relation is reflexive, symmetric, transitive, or none of these. Justify your answers. (Brief explanations are all that's required.)
    Let X = {a, b, c} and P(X) be the power set of X. A binary relation R is defined on P (X) as follows:
    for all A, B &#61646; P (X), A R B &#61659; n(A) < n(B) (that is, the number of elements in A is less than the number of elements in B.

    © BrainMass Inc. brainmass.com November 24, 2021, 11:04 am ad1c9bdddf
    https://brainmass.com/math/discrete-math/discrete-math-binary-relations-determined-6214

    Attachments

    Solution Preview

    Please see the attached file for the complete solution.
    Thanks for using BrainMass.

    2. a. Please see the following graph.

    b. No. Since
    c. No. Since , but
    d. No. Since ...

    Solution Summary

    Binary relations are graphed and their properties determined. The relation of reflexive and symmetric is determined.

    $2.49

    ADVERTISEMENT