Hasse Diagram Challenge

6

Poset Parameters

Parameters

Poset Properties

Nodes: 6

Relations: 0

Minimal Nodes: -

Maximal Nodes: -

How to Use This Experiment

Instructions

• Click on two vertices to add a directed edge (covering relation).

• Build the Hasse diagram one edge at a time.

• Use "Check Diagram" to verify your construction.

• "New Relation" generates a different partial order.

• "Clear Diagram" removes all edges you've drawn.

• "Undo" removes the last edge you added.

Adjust Parameters

• Click the floating controls button to open parameters.

• Change the number of nodes or relation type.

• Different relation types provide different challenges.

• Easy Mode: Subsets of {1,2,3} - fewer nodes to manage.

• Hard Mode: Subsets of {1,2,3,4} - more complex relationships.

Tips

• Hasse diagrams show only covering relations (direct connections).

• Look for minimal and maximal elements.

• Transitivity is implied - don't draw transitive edges.

Partial Orders

A partial order is a binary relation that is reflexive, antisymmetric, and transitive.

Properties:

  • Reflexive: a ≤ a for all a
  • Antisymmetric: if a ≤ b and b ≤ a, then a = b
  • Transitive: if a ≤ b and b ≤ c, then a ≤ c

Examples:

  • Subset relation on power sets
  • Divisibility on integers
  • Less than or equal on real numbers

Hasse Diagrams

A Hasse diagram is a visual representation of a partial order showing only covering relations.

Key Elements:

  • Minimal: no element below it
  • Maximal: no element above it
  • Covering: direct relation without intermediate

Construction Rules:

  • Show only covering relations
  • Arrange elements vertically by order
  • Omit reflexive and transitive edges