Final answer:
The intersection of the set ∩{(1,2), (2,3),(1,3)} is the empty set as there are no common elements. For an order relation, the intersection with itself retains the same relation.
Step-by-step explanation:
The question asks about the intersection of a family of relations and whether the intersection of a transitive and irreflexive relation results in the original relation. Specifically, it refers to the intersection of the set ∩{(1,2), (2,3),(1,3)}. In this context, the intersection of relations is the set of ordered pairs that are common to all relations in the family.
However, for the provided set of pairs, there is no common element among all three, so the intersection would be the empty set. If a relation is both transitive and irreflexive, it is considered an order relation. The intersection of an order relation with itself will indeed result in the same order relation, confirming its properties.