# Discrete mathematics

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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