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In discrete mathematics and set theory, is empty relation a partial order relation?
This is because you confuse the similarities and differences between empty sets and empty relationships.

Satisfying reflexivity means that all elements in the set must satisfy.

However, there are no elements in the empty set, which can be considered as satisfying reflexivity, so the empty relationship is a partial order relationship.

For non-empty sets, empty relations obviously do not satisfy reflexivity, so they are not partial ordered relations.