Hasse Diagram

algebra

Hasse Diagram

A Hasse diagram is a diagram for equivalence relations that is used to show the relations between elements.

Relations are represented as a graph-like structure. However, since this diagram is specifically for equivalence relations, the default connections which are present in all equivalence relations are omitted:

• reflexive: Since all elements in an equivalence relation are related to themselves, their relations are omitted.
• symmetric: Since all elements in an equivalence relation are symmetric, back-connections are omitted.
• transitive: Since all elements in an equivalence relation are transitive, their transitive inter-connections are omitted.

Example: Hasse diagram for $(P(\{1,2,3\},\subseteq ))$, where $P(\{1,2,3\})$ is the power set of $\{1,2,3\}$.