{"id":3080,"date":"2025-06-06T09:51:13","date_gmt":"2025-06-06T09:51:13","guid":{"rendered":"https:\/\/diznr.com\/?p=3080"},"modified":"2025-06-06T09:51:13","modified_gmt":"2025-06-06T09:51:13","slug":"part-09-discrete-mathematics-in-hindi-short-trick-for-transitive-relation-to-quick-solve","status":"publish","type":"post","link":"https:\/\/www.reilsolar.com\/pdf\/part-09-discrete-mathematics-in-hindi-short-trick-for-transitive-relation-to-quick-solve\/","title":{"rendered":"Part 09- Discrete mathematics in Hindi – Short trick for transitive relation to solve quick."},"content":{"rendered":"

Part 09- Discrete mathematics in Hindi – Short trick for transitive relation to solve quick.<\/p>\n

[fvplayer id=”242″]<\/p>\n

\u091f\u094d\u0930\u093e\u0902\u091c\u093c\u093f\u091f\u093f\u0935 \u0930\u093f\u0932\u0947\u0936\u0928<\/strong> (\u0938\u093e\u0902\u0915\u094d\u0930\u092e\u093f\u0915 \u0938\u0902\u092c\u0902\u0927) \u0917\u0923\u093f\u0924 \u092e\u0947\u0902 \u090f\u0915 \u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u0905\u0935\u0927\u093e\u0930\u0923\u093e \u0939\u0948, \u0935\u093f\u0936\u0947\u0937 \u0930\u0942\u092a \u0938\u0947 \u0921\u093f\u0938\u094d\u0915\u094d\u0930\u0940\u091f \u092e\u0948\u0925\u092e\u0947\u091f\u093f\u0915\u094d\u0938<\/strong> \u092e\u0947\u0902\u0964 \u092f\u0926\u093f \u0915\u093f\u0938\u0940 \u0938\u0947\u091f AA<\/span>A<\/span><\/span><\/span><\/span> \u092a\u0930 \u090f\u0915 \u0938\u0902\u092c\u0902\u0927 RR<\/span>R<\/span><\/span><\/span><\/span> \u0915\u0947 \u0932\u093f\u090f, \u092f\u0926\u093f aRbaRb<\/span>a<\/span>R<\/span>b<\/span><\/span><\/span><\/span> \u0914\u0930 bRcbRc<\/span>b<\/span>R<\/span>c<\/span><\/span><\/span><\/span> \u0938\u0947 aRcaRc<\/span>a<\/span>R<\/span>c<\/span><\/span><\/span><\/span> \u0939\u094b\u0924\u093e \u0939\u0948, \u0924\u094b RR<\/span>R<\/span><\/span><\/span><\/span> \u0915\u094b \u091f\u094d\u0930\u093e\u0902\u091c\u093c\u093f\u091f\u093f\u0935 \u0915\u0939\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964<\/p>\n

\u091f\u094d\u0930\u093e\u0902\u091c\u093c\u093f\u091f\u093f\u0935\u093f\u091f\u0940 \u0915\u0940 \u091c\u093e\u0901\u091a \u0915\u0947 \u0932\u093f\u090f \u0936\u0949\u0930\u094d\u091f\u0915\u091f \u0935\u093f\u0927\u093f:<\/strong><\/p>\n

    \n
  1. \n

    \u0938\u0902\u092c\u0902\u0927 \u0915\u0940 \u0938\u0942\u091a\u0940 \u092c\u0928\u093e\u090f\u0902:<\/strong> \u0938\u092c\u0938\u0947 \u092a\u0939\u0932\u0947, \u0926\u093f\u090f \u0917\u090f \u0938\u0902\u092c\u0902\u0927 RR<\/span>R<\/span><\/span><\/span><\/span> \u0915\u0947 \u0938\u092d\u0940 \u092f\u0941\u0917\u094d\u092e\u094b\u0902 (pairs) \u0915\u094b \u0938\u0942\u091a\u0940\u092c\u0926\u094d\u0927 \u0915\u0930\u0947\u0902\u0964<\/p>\n<\/li>\n

  2. \n

    \u092e\u0927\u094d\u092f\u0935\u0930\u094d\u0924\u0940 \u0924\u0924\u094d\u0935 \u0916\u094b\u091c\u0947\u0902:<\/strong> \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u092f\u0941\u0917\u094d\u092e (a,b)(a, b)<\/span>(<\/span>a<\/span>,<\/span>b<\/span>)<\/span><\/span><\/span><\/span> \u0915\u0947 \u0932\u093f\u090f, \u0910\u0938\u093e bb<\/span>b<\/span><\/span><\/span><\/span> \u0916\u094b\u091c\u0947\u0902 \u091c\u094b \u0915\u093f\u0938\u0940 \u0905\u0928\u094d\u092f \u092f\u0941\u0917\u094d\u092e (b,c)(b, c)<\/span>(<\/span>b<\/span>,<\/span>c<\/span>)<\/span><\/span><\/span><\/span> \u092e\u0947\u0902 \u0909\u092a\u0938\u094d\u0925\u093f\u0924 \u0939\u094b\u0964<\/p>\n<\/li>\n

  3. \n

    \u0928\u092f\u093e \u092f\u0941\u0917\u094d\u092e \u092c\u0928\u093e\u090f\u0902:<\/strong> \u092f\u0926\u093f (a,b)(a, b)<\/span>(<\/span>a<\/span>,<\/span>b<\/span>)<\/span><\/span><\/span><\/span> \u0914\u0930 (b,c)(b, c)<\/span>(<\/span>b<\/span>,<\/span>c<\/span>)<\/span><\/span><\/span><\/span> \u092e\u094c\u091c\u0942\u0926 \u0939\u0948\u0902, \u0924\u094b (a,c)(a, c)<\/span>(<\/span>a<\/span>,<\/span>c<\/span>)<\/span><\/span><\/span><\/span> \u092d\u0940 \u0938\u0902\u092c\u0902\u0927 RR<\/span>R<\/span><\/span><\/span><\/span> \u092e\u0947\u0902 \u0939\u094b\u0928\u093e \u091a\u093e\u0939\u093f\u090f\u0964<\/p>\n<\/li>\n

  4. \n

    \u0938\u0924\u094d\u092f\u093e\u092a\u0928 \u0915\u0930\u0947\u0902:<\/strong> \u092f\u0926\u093f \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0938\u0902\u092d\u0935 (a,c)(a, c)<\/span>(<\/span>a<\/span>,<\/span>c<\/span>)<\/span><\/span><\/span><\/span> \u092f\u0941\u0917\u094d\u092e RR<\/span>R<\/span><\/span><\/span><\/span> \u092e\u0947\u0902 \u092e\u094c\u091c\u0942\u0926 \u0939\u0948, \u0924\u094b \u0938\u0902\u092c\u0902\u0927 \u091f\u094d\u0930\u093e\u0902\u091c\u093c\u093f\u091f\u093f\u0935 \u0939\u0948; \u0905\u0928\u094d\u092f\u0925\u093e \u0928\u0939\u0940\u0902\u0964<\/p>\n<\/li>\n<\/ol>\n

    \u0909\u0926\u093e\u0939\u0930\u0923:<\/strong><\/p>\n

    \u092e\u093e\u0928 \u0932\u0947\u0902 \u0915\u093f \u0938\u0947\u091f A={1,2,3}A = \\{1, 2, 3\\}<\/span>A<\/span>=<\/span><\/span>{<\/span>1<\/span>,<\/span>2<\/span>,<\/span>3<\/span>}<\/span><\/span><\/span><\/span> \u0914\u0930 \u0938\u0902\u092c\u0902\u0927 R={(1,2),(2,3),(1,3)}R = \\{(1, 2), (2, 3), (1, 3)\\}<\/span>R<\/span>=<\/span><\/span>{(<\/span>1<\/span>,<\/span>2<\/span>)<\/span>,<\/span>(<\/span>2<\/span>,<\/span>3<\/span>)<\/span>,<\/span>(<\/span>1<\/span>,<\/span>3<\/span>)}<\/span><\/span><\/span><\/span> \u0939\u0948\u0964<\/p>\n