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    Discrete mathematics

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    Define a relation D on the set of all people in the following way: x D y if and only if x = y or x is a descendent of y. Which of the properties does this relation have? For each property, explain why the relation has the property, or give a counterexample.
    Equivalence relation
    Partial order relation
    Total order relation

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    Solution Preview

    Assume that the set X represents the set of all people.

    Reflexive: Yes
    Because for any x in X, x = x and thus x D x.

    Symmetric: No
    Suppose y is the son of x, then y D x holds, but x D y does not hold.

    Transitive: Yes
    If x D y and y D z, ...

    Solution Summary

    In this solution, we outline the properties that a given relation has and explain why it has them.