An equivalence relation partitions its set into classes with no overlaps and nothing left out. Why do reflexivity, symmetry and transitivity together force that structure?

A. Because reflexivity leaves nothing out, and symmetry with transitivity forbid overlap.

Reflexivity puts every element in its own class, so nothing is left out. For overlaps: if [a] and [b] share z then a ~ z and b ~ z, symmetry and transitivity give a ~ b, and the classes coincide. All three are load-bearing, 'is less than' is transitive alone and partitions nothing. The converse holds too, so partitions and equivalence relations are one idea.