Let P be the set of all people who have ever lived and define a relation R on P as follows: For every
, is an ancestor of s or
Is R a partial order relation? Prove or give a counterexample.
To prove or give the counter example for to be a partial order relation.
Let be the set of all people who have ever lived and define a relation on as follows: for all , is an ancestor of or .
A partial order relation is a relation which is reflexive, antisymmetric and transitive.
So let us verify the following all three properties for to be a partial order relation.
Reflexivity- Suppose because . Therefore the relation is reflexive.
Antisymmetry- Suppose such that is an ancestor of or .
And is an ancestor of or
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