{"id":3038,"date":"2025-06-07T14:54:11","date_gmt":"2025-06-07T14:54:11","guid":{"rendered":"https:\/\/diznr.com\/?p=3038"},"modified":"2025-06-07T14:54:11","modified_gmt":"2025-06-07T14:54:11","slug":"day-03part-04-discrete-mathematics-for-computer-science-in-hindi-example-on-diagram-hasse","status":"publish","type":"post","link":"https:\/\/www.reilsolar.com\/pdf\/day-03part-04-discrete-mathematics-for-computer-science-in-hindi-example-on-diagram-hasse\/","title":{"rendered":"Day 03Part 04- Discrete mathematics for computer science in hindi- Example on Hasse Diagram."},"content":{"rendered":"

Day 03Part 04- Discrete mathematics for computer science in hindi- Example on Hasse Diagram.<\/p>\n

[fvplayer id=”227″]<\/p>\n

\u00a0Day 03 | Part 04 \u2013 \u0921\u093f\u0938\u094d\u0915\u094d\u0930\u0940\u091f \u092e\u0948\u0925\u092e\u0947\u091f\u093f\u0915\u094d\u0938 (Discrete Mathematics) for Computer Science<\/strong><\/h3>\n

\u00a0Hasse Diagram \u0915\u093e \u0909\u0926\u093e\u0939\u0930\u0923 (Example on Hasse Diagram)<\/strong><\/h3>\n

\u00a0Hasse Diagram \u0915\u094d\u092f\u093e \u0939\u0948?<\/strong><\/h3>\n

Hasse Diagram \u090f\u0915 \u0917\u094d\u0930\u093e\u092b\u093f\u0915\u0932 \u0930\u093f\u092a\u094d\u0930\u0947\u091c\u0947\u0902\u091f\u0947\u0936\u0928<\/strong> \u0939\u0948 \u091c\u094b \u0915\u093f\u0938\u0940 Partially Ordered Set (Poset)<\/strong> \u0915\u094b \u0926\u093f\u0916\u093e\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0909\u092a\u092f\u094b\u0917 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964<\/p>\n

\u00a0\u0907\u0938\u092e\u0947\u0902 \u0928\u094b\u0921\u094d\u0938 (Nodes) \u0914\u0930 \u090f\u091c\u0947\u0938 (Edges)<\/strong> \u0939\u094b\u0924\u0947 \u0939\u0948\u0902\u0964
\u0938\u0940\u0927\u0947 \u0915\u0928\u0947\u0915\u094d\u0936\u0928\u094d\u0938<\/strong> \u0926\u093f\u0916\u093e\u090f \u091c\u093e\u0924\u0947 \u0939\u0948\u0902, \u0932\u0947\u0915\u093f\u0928 \u091f\u094d\u0930\u093e\u0902\u091c\u093f\u091f\u093f\u0935 \u090f\u091c\u0947\u0938<\/strong> \u0939\u091f\u093e\u090f \u091c\u093e\u0924\u0947 \u0939\u0948\u0902\u0964
\u091b\u094b\u091f\u0947 \u0938\u0947 \u092c\u0921\u093c\u0947 \u090f\u0932\u093f\u092e\u0947\u0902\u091f\u094d\u0938<\/strong> \u0924\u0915 \u0915\u0928\u0947\u0915\u094d\u0936\u0928 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902\u0964<\/p>\n

\u00a0Hasse Diagram \u092c\u0928\u093e\u0928\u0947 \u0915\u0947 \u0938\u094d\u091f\u0947\u092a\u094d\u0938<\/strong><\/h3>\n

\u00a0\u0926\u093f\u090f \u0917\u090f \u0938\u0902\u092c\u0902\u0927 (Relation)<\/strong> \u0915\u0947 \u0906\u0927\u093e\u0930 \u092a\u0930 \u0906\u0930\u0947\u0916 (Diagram) \u092c\u0928\u093e\u090f\u0902\u0964
\u0938\u092c\u0938\u0947 \u091b\u094b\u091f\u0947 \u0938\u0947 \u0938\u092c\u0938\u0947 \u092c\u0921\u093c\u0947 \u090f\u0932\u093f\u092e\u0947\u0902\u091f\u094d\u0938<\/strong> \u0915\u094b \u0915\u0928\u0947\u0915\u094d\u091f \u0915\u0930\u0947\u0902\u0964
\u091f\u094d\u0930\u093e\u0902\u091c\u093f\u091f\u093f\u0935 \u090f\u091c\u0947\u0938 \u0915\u094b \u0939\u091f\u093e\u090f\u0902<\/strong> (\u091c\u094b \u092a\u0939\u0932\u0947 \u0938\u0947 \u090f\u0915 \u0936\u0949\u0930\u094d\u091f\u0930 \u092a\u093e\u0925 \u0938\u0947 \u091c\u0941\u0921\u093c\u0947 \u0939\u0948\u0902)\u0964<\/p>\n

\u00a0\u0909\u0926\u093e\u0939\u0930\u0923 1: \u0938\u0947\u091f {1, 2, 4, 8} \u0915\u093e Hasse Diagram<\/strong><\/h3>\n

\u0938\u0902\u092c\u0902\u0927:<\/strong> Divisibility (|)<\/strong> \u092a\u0930 \u0906\u0927\u093e\u0930\u093f\u0924<\/p>\n

    \n
  • 1 | 2 (1, 2 \u0938\u0947 \u091b\u094b\u091f\u093e \u0939\u0948)<\/li>\n
  • 2 | 4 (2, 4 \u0938\u0947 \u091b\u094b\u091f\u093e \u0939\u0948)<\/li>\n
  • 4 | 8 (4, 8 \u0938\u0947 \u091b\u094b\u091f\u093e \u0939\u0948)<\/li>\n<\/ul>\n

    Hasse Diagram:<\/strong><\/h3>\n
    \n
    8
    \n|
    \n4
    \n|
    \n2
    \n|
    \n1
    \n<\/span><\/code><\/div>\n<\/div>\n

    \u092f\u0939 \u090f\u0915 Poset \u0939\u0948!<\/strong><\/p>\n

    \u00a0\u0909\u0926\u093e\u0939\u0930\u0923 2: \u0938\u0947\u091f {a, b, c, d} \u0915\u0947 \u0938\u093e\u0925<\/strong><\/h3>\n

    \u0930\u093f\u0932\u0947\u0936\u0928:<\/strong> {(a, b), (a, c), (b, d), (c, d)}<\/code><\/p>\n

    Hasse Diagram:<\/strong><\/h3>\n
    \n
    a<\/span>
    \n\/ \\
    \nb<\/span> c
    \n\\ \/
    \nd
    \n<\/code><\/div>\n<\/div>\n

    \u00a0\u092f\u0939 Partially Ordered Set (Poset)<\/strong> \u0939\u0948\u0964<\/p>\n

    \u00a0\u0915\u094d\u092f\u093e Hasse Diagram \u090f\u0915 Lattice \u0939\u0948?<\/strong><\/h2>\n

    \u0905\u0917\u0930 \u0939\u0930 \u0926\u094b \u090f\u0932\u093f\u092e\u0947\u0902\u091f\u094d\u0938 \u0915\u093e Least Upper Bound (LUB) \u0914\u0930 Greatest Lower Bound (GLB) \u0939\u094b\u0924\u093e \u0939\u0948, \u0924\u094b \u092f\u0939 \u090f\u0915 Lattice \u0939\u0948\u0964<\/strong>
    \u092a\u0939\u0932\u0947 Hasse Diagram \u092c\u0928\u093e\u090f\u0902, \u092b\u093f\u0930 \u0926\u0947\u0916\u0947\u0902 \u0915\u093f \u0939\u0930 \u091c\u094b\u0921\u093c\u0947 (pair) \u0915\u0947 \u0932\u093f\u090f LUB \u0914\u0930 GLB \u0939\u0948\u0902 \u092f\u093e \u0928\u0939\u0940\u0902\u0964<\/strong><\/p>\n

    \u00a0\u0928\u093f\u0937\u094d\u0915\u0930\u094d\u0937:<\/strong><\/h3>\n

    \u00a0Hasse Diagram Poset \u0915\u094b \u0935\u093f\u091c\u093c\u0941\u0905\u0932\u093e\u0907\u091c\u093c \u0915\u0930\u0928\u0947<\/strong> \u0915\u093e \u0938\u0930\u0932 \u0924\u0930\u0940\u0915\u093e \u0939\u0948\u0964
    Divisibility, Set Inclusion, \u0914\u0930 \u0905\u0928\u094d\u092f \u0906\u0930\u094d\u0921\u0930 \u0930\u093f\u0932\u0947\u0936\u0902\u0938<\/strong> \u0915\u0947 \u0932\u093f\u090f \u0909\u092a\u092f\u094b\u0917\u0940 \u0939\u0948\u0964
    Lattice \u0915\u0940 \u092a\u0939\u091a\u093e\u0928 \u0915\u0930\u0928\u0947<\/strong> \u092e\u0947\u0902 \u092e\u0926\u0926 \u0915\u0930\u0924\u093e \u0939\u0948\u0964<\/p>\n

    \u00a0\u0915\u094d\u092f\u093e \u0906\u092a \u0914\u0930 \u0909\u0926\u093e\u0939\u0930\u0923 \u092f\u093e \u0938\u094d\u091f\u0947\u092a-\u092c\u093e\u092f-\u0938\u094d\u091f\u0947\u092a \u0938\u0949\u0932\u094d\u092f\u0942\u0936\u0928 \u091a\u093e\u0939\u0924\u0947 \u0939\u0948\u0902?<\/strong><\/p>\n

    \u092c\u093f\u0932\u0915\u0941\u0932! \u092f\u0939 \u0930\u0939\u093e Day 03 Part 04 \u2013 Discrete Mathematics for Computer Science in Hindi<\/strong>, \u091c\u093f\u0938\u092e\u0947\u0902 \u0939\u092e Hasse Diagram<\/strong> \u0915\u093e \u090f\u0915 \u0906\u0938\u093e\u0928 \u0909\u0926\u093e\u0939\u0930\u0923 \u0939\u093f\u0902\u0926\u0940 \u092e\u0947\u0902 \u0938\u092e\u091d\u0947\u0902\u0917\u0947\u0964<\/p>\n

    \n

    \ud83d\udcd8 Hasse Diagram \u0915\u094d\u092f\u093e \u0939\u0948?<\/strong><\/h2>\n

    Hasse Diagram<\/strong> \u090f\u0915 \u0917\u094d\u0930\u093e\u092b\u093c\u093f\u0915\u0932 \u0924\u0930\u0940\u0915\u093e \u0939\u0948 \u091c\u093f\u0938\u0938\u0947 \u0939\u092e \u0915\u093f\u0938\u0940 partially ordered set (poset)<\/strong> \u0915\u094b \u092c\u093f\u0928\u093e \u0926\u0941\u0939\u0930\u093e\u090f \u0939\u0941\u090f \u0924\u0924\u094d\u0935\u094b\u0902 \u0914\u0930 \u0909\u0928\u0915\u0947 order relations<\/strong> \u0915\u0947 \u0938\u093e\u0925 \u0926\u0930\u094d\u0936\u093e\u0924\u0947 \u0939\u0948\u0902\u0964<\/p>\n

    \n

    \ud83d\udd37 Step-by-Step: Hasse Diagram \u0915\u093e \u0909\u0926\u093e\u0939\u0930\u0923<\/strong><\/h3>\n

    \u092e\u093e\u0928 \u0932\u0940\u091c\u093f\u090f \u0939\u092e\u093e\u0930\u0947 \u092a\u093e\u0938 \u090f\u0915 \u0938\u0947\u091f \u0939\u0948:<\/p>\n

    A={1,2,4,8}A = \\{1, 2, 4, 8\\}<\/span>A<\/span>=<\/span><\/span>{<\/span>1<\/span>,<\/span>2<\/span>,<\/span>4<\/span>,<\/span>8<\/span>}<\/span><\/span><\/span><\/span><\/span><\/p>\n

    \u0914\u0930 \u0930\u093f\u0932\u0947\u0936\u0928 \u0939\u0948: a \u2264 b \u092f\u0926\u093f a \u092c\u091f\u093e b \u0939\u094b\u0924\u093e \u0939\u0948 (i.e. divisibility relation)<\/strong><\/p>\n

    \n

    \ud83d\udd39 Step 1: Pairs \u0928\u093f\u0915\u093e\u0932\u094b \u091c\u093f\u0928\u092e\u0947\u0902 a \u2264 b \u0939\u094b\u0924\u093e \u0939\u0948<\/strong><\/h3>\n

    (\u0914\u0930 a \u2260 b)<\/p>\n

      \n
    • \n

      1 divides 2, 4, 8 \u21d2 (1,2), (1,4), (1,8)<\/p>\n<\/li>\n

    • \n

      2 divides 4, 8 \u21d2 (2,4), (2,8)<\/p>\n<\/li>\n

    • \n

      4 divides 8 \u21d2 (4,8)<\/p>\n<\/li>\n<\/ul>\n

      \n

      \ud83d\udd39 Step 2: Covering Pairs \u0916\u094b\u091c\u094b<\/strong><\/h3>\n

      \u0939\u092e \u0915\u0947\u0935\u0932 \u0935\u094b edges \u0932\u0947\u0902\u0917\u0947 \u091c\u093f\u0928\u092e\u0947\u0902 \u0915\u094b\u0908 intermediate node \u0928\u0939\u0940\u0902<\/strong> \u0939\u0948\u0964 \u092f\u093e\u0928\u0940, \u0939\u092e transitive pairs \u0915\u094b \u091b\u094b\u0921\u093c \u0926\u0947\u0902\u0917\u0947\u0964<\/p>\n

        \n
      • \n

        (1,2), (2,4), (4,8) \u2705<\/p>\n<\/li>\n

      • \n

        (1,4) \u0914\u0930 (1,8) transitive<\/strong> \u0939\u0948\u0902 \u21d2 \u274c \u091b\u094b\u0921\u093c \u0926\u094b<\/p>\n<\/li>\n

      • \n

        (2,8) \u092d\u0940 transitive<\/strong> \u21d2 \u274c \u091b\u094b\u0921\u093c \u0926\u094b<\/p>\n<\/li>\n<\/ul>\n

        \n

        \ud83d\udd39 Step 3: Hasse Diagram \u092c\u0928\u093e\u0913<\/strong><\/h3>\n
          \n
        • \n

          \u0938\u092c\u0938\u0947 \u0928\u0940\u091a\u0947 1<\/p>\n<\/li>\n

        • \n

          \u090a\u092a\u0930 2<\/p>\n<\/li>\n

        • \n

          \u092b\u093f\u0930 4<\/p>\n<\/li>\n

        • \n

          \u0938\u092c\u0938\u0947 \u090a\u092a\u0930 8<\/p>\n<\/li>\n<\/ul>\n

          Edges:<\/strong><\/p>\n

            \n
          • \n

            1 \u2192 2<\/p>\n<\/li>\n

          • \n

            2 \u2192 4<\/p>\n<\/li>\n

          • \n

            4 \u2192 8<\/p>\n<\/li>\n<\/ul>\n

            \n
            markdown<\/div>\n
            \n
            \n