{"id":3036,"date":"2025-06-06T14:51:53","date_gmt":"2025-06-06T14:51:53","guid":{"rendered":"https:\/\/diznr.com\/?p=3036"},"modified":"2025-06-06T14:51:53","modified_gmt":"2025-06-06T14:51:53","slug":"day-03part-05-discrete-mathematics-for-computer-science-finding-relation-from-diagram-hasse","status":"publish","type":"post","link":"https:\/\/www.reilsolar.com\/pdf\/day-03part-05-discrete-mathematics-for-computer-science-finding-relation-from-diagram-hasse\/","title":{"rendered":"Day 03Part 05- Discrete mathematics for computer science – Finding Relation from Hasse Diagram."},"content":{"rendered":"

Day 03Part 05- Discrete mathematics for computer science – Finding Relation from Hasse Diagram.<\/p>\n

[fvplayer id=”226″]<\/p>\n

Discrete Mathematics – Finding Relations from Hasse Diagram<\/strong><\/h3>\n

What is a Hasse Diagram?<\/strong><\/h3>\n

A Hasse Diagram<\/strong> is a graphical representation of a partially ordered set<\/strong> (poset). It simplifies the relation by removing self-loops, transitive edges, and directions.<\/p>\n

\u00a0Key Components of a Hasse Diagram:<\/strong><\/h3>\n
    \n
  1. Vertices (Nodes):<\/strong> Represent elements of the set.<\/li>\n
  2. Edges (Lines):<\/strong> Show the relation between elements. If there’s an edge from a<\/strong> to b<\/strong>, then a \u2264 b<\/strong>.<\/li>\n
  3. No Self-Loops:<\/strong> A node doesn’t relate to itself.<\/li>\n
  4. No Transitive Edges:<\/strong> If a \u2264 b<\/strong> and b \u2264 c<\/strong>, the direct edge a \u2264 c<\/strong> is removed.<\/li>\n
  5. No Direction Arrows:<\/strong> Direction is understood bottom to top.<\/li>\n<\/ol>\n

    \u00a0Steps to Find Relations from Hasse Diagram:<\/strong><\/h3>\n
      \n
    1. Identify All Elements:<\/strong> Write all elements in the set.<\/li>\n
    2. List Minimal Elements:<\/strong> Start from the bottom of the diagram.<\/li>\n
    3. Follow Relations:<\/strong> List the ordered pairs (a,b)(a, b)<\/span>(<\/span>a<\/span>,<\/span>b<\/span>)<\/span><\/span><\/span><\/span> where there is a direct edge from a<\/strong> to b<\/strong>.<\/li>\n
    4. Include Reflexive Pairs:<\/strong> If reflexivity is needed, add (a,a)(a, a)<\/span>(<\/span>a<\/span>,<\/span>a<\/span>)<\/span><\/span><\/span><\/span> for each element.<\/li>\n
    5. Check Transitivity:<\/strong> Ensure no missing pairs if transitivity is considered.<\/li>\n<\/ol>\n

      \u00a0Example:<\/strong><\/h3>\n

      Given a Hasse diagram with elements {1, 2, 3, 4}<\/strong>:<\/p>\n

      \n
      4
      \n\/ \\
      \n2 3
      \n\\ \/
      \n1
      \n<\/span><\/code><\/div>\n<\/div>\n

      Relation Set (R):<\/strong><\/p>\n