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