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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.
Reflexive
Symmetric
Transitive
Antisymmetric
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.

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