Partial Order and Hasse Diagram

Procedure

This experiment allows you to practice constructing Hasse diagrams by clicking on vertices to create covering relations (direct edges) for given partial orders.

Interactive Hasse Diagram Construction

Objective: Build the correct Hasse diagram by adding edges one at a time between the given vertices.

How to Use:

  1. Adding Edges: Click on two vertices in sequence to create a directed edge representing a covering relation in the Hasse diagram.

    • First click selects the source vertex
    • Second click selects the target vertex and creates the edge
    • The edge represents a covering relation from the first vertex to the second
  2. Checking Your Work:

    • Click the "Check Diagram" button to verify if your constructed Hasse diagram is correct
    • The system will provide feedback indicating whether your diagram matches the expected solution
    • Correct edges will be highlighted, and missing or incorrect edges will be indicated
  3. Getting Help:

    • Click the "Hint" button to get guidance on the next edge to add
    • Hints will help you understand the structure of the partial order
  4. Managing Your Progress:

    • Use "Undo" to remove the last edge you added
    • Use "Clear Diagram" to remove all edges and start over
    • Use "New Relation" to generate a completely new partial order to practice with
  5. Adjusting Parameters:

    • Click the floating controls button (⚙️) to access parameter settings
    • Change the number of nodes (4-8) to adjust difficulty
    • Select different relation types:
      • Easy Mode: Subsets of {1,2,3} - simpler relationships
      • Hard Mode: Subsets of {1,2,3,4} - more complex relationships
      • Divisors Mode: Divisibility relations between numbers
  6. Understanding the Display:

    • The Poset Properties panel shows information about your current diagram
    • Minimal and maximal elements are identified
    • Total number of relations is tracked

Tips for Success:

  • Remember that Hasse diagrams show only covering relations (direct connections)
  • Look for minimal elements (no elements below them) and maximal elements (no elements above them)
  • Don't add transitive edges - only direct covering relations
  • Use the hint system if you get stuck