{"id":2938,"date":"2025-06-05T07:01:06","date_gmt":"2025-06-05T07:01:06","guid":{"rendered":"https:\/\/diznr.com\/?p=2938"},"modified":"2025-06-05T07:01:06","modified_gmt":"2025-06-05T07:01:06","slug":"equivalence-concept-gate-2021-discrete-mathematics-previous-year-paper-hindi-in","status":"publish","type":"post","link":"https:\/\/www.reilsolar.com\/pdf\/equivalence-concept-gate-2021-discrete-mathematics-previous-year-paper-hindi-in\/","title":{"rendered":"Equivalence concept- GATE 2025 Discrete mathematics previous year paper in Hindi"},"content":{"rendered":"<p>Equivalence concept- GATE 2025 Discrete mathematics previous year paper in Hindi<\/p>\n<p>[fvplayer id=&#8221;179&#8243;]<\/p>\n<p data-start=\"0\" data-end=\"454\"><strong data-start=\"0\" data-end=\"25\">\u0924\u0941\u0932\u094d\u092f\u0924\u093e (Equivalence)<\/strong> \u0924\u093e\u0930\u094d\u0915\u093f\u0915 \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, \u091c\u094b \u0926\u094b \u0915\u0925\u0928\u094b\u0902 \u092f\u093e \u0938\u0942\u0924\u094d\u0930\u094b\u0902 \u0915\u0947 \u0938\u092e\u093e\u0928 \u0938\u0924\u094d\u092f-\u092e\u0942\u0932\u094d\u092f \u0915\u094b \u0928\u093f\u0930\u0942\u092a\u093f\u0924 \u0915\u0930\u0924\u0940 \u0939\u0948\u0964 \u092f\u0926\u093f \u0926\u094b \u0924\u093e\u0930\u094d\u0915\u093f\u0915 \u0915\u0925\u0928 \u0938\u092d\u0940 \u0938\u0902\u092d\u093e\u0935\u093f\u0924 \u0938\u094d\u0925\u093f\u0924\u093f\u092f\u094b\u0902 \u092e\u0947\u0902 \u0938\u092e\u093e\u0928 \u0938\u0924\u094d\u092f-\u092e\u0942\u0932\u094d\u092f \u0930\u0916\u0924\u0947 \u0939\u0948\u0902, \u0924\u094b \u0935\u0947 \u0924\u0941\u0932\u094d\u092f \u0915\u0939\u0932\u093e\u0924\u0947 \u0939\u0948\u0902\u0964 \u0909\u0926\u093e\u0939\u0930\u0923 \u0915\u0947 \u0932\u093f\u090f, \u0915\u0925\u0928 <span class=\"katex\"><span class=\"katex-mathml\">P\u2192QP \\rightarrow Q<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">P<\/span><span class=\"mrel\">\u2192<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">Q<\/span><\/span><\/span><\/span> (\u092f\u0926\u093f <span class=\"katex\"><span class=\"katex-mathml\">PP<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">P<\/span><\/span><\/span><\/span> \u0924\u094b <span class=\"katex\"><span class=\"katex-mathml\">QQ<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">Q<\/span><\/span><\/span><\/span>) \u0914\u0930 \u0909\u0938\u0915\u093e \u092a\u094d\u0930\u0924\u093f\u0932\u094b\u092e <span class=\"katex\"><span class=\"katex-mathml\">\u00acQ\u2192\u00acP\\neg Q \\rightarrow \\neg P<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">\u00ac<\/span><span class=\"mord mathnormal\">Q<\/span><span class=\"mrel\">\u2192<\/span><\/span><span class=\"base\"><span class=\"mord\">\u00ac<\/span><span class=\"mord mathnormal\">P<\/span><\/span><\/span><\/span> (\u092f\u0926\u093f \u0928\u0939\u0940\u0902 <span class=\"katex\"><span class=\"katex-mathml\">QQ<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">Q<\/span><\/span><\/span><\/span> \u0924\u094b \u0928\u0939\u0940\u0902 <span class=\"katex\"><span class=\"katex-mathml\">PP<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">P<\/span><\/span><\/span><\/span>) \u0938\u092d\u0940 \u0938\u094d\u0925\u093f\u0924\u093f\u092f\u094b\u0902 \u092e\u0947\u0902 \u0938\u092e\u093e\u0928 \u0938\u0924\u094d\u092f-\u092e\u0942\u0932\u094d\u092f \u0930\u0916\u0924\u0947 \u0939\u0948\u0902, \u0907\u0938\u0932\u093f\u090f \u0935\u0947 \u0924\u093e\u0930\u094d\u0915\u093f\u0915 \u0930\u0942\u092a \u0938\u0947 \u0924\u0941\u0932\u094d\u092f \u0939\u0948\u0902\u0964<\/p>\n<p data-start=\"456\" data-end=\"508\"><strong data-start=\"456\" data-end=\"508\">GATE 2025 \u092a\u0930\u0940\u0915\u094d\u0937\u093e \u092e\u0947\u0902 \u0924\u0941\u0932\u094d\u092f\u0924\u093e \u0938\u0947 \u0938\u0902\u092c\u0902\u0927\u093f\u0924 \u092a\u094d\u0930\u0936\u094d\u0928:<\/strong><\/p>\n<p data-start=\"510\" data-end=\"686\">GATE 2025 \u0915\u0940 \u092a\u0930\u0940\u0915\u094d\u0937\u093e \u092e\u0947\u0902 \u0924\u0941\u0932\u094d\u092f\u0924\u093e \u0938\u0947 \u0938\u0902\u092c\u0902\u0927\u093f\u0924 \u092a\u094d\u0930\u0936\u094d\u0928 \u092a\u0942\u091b\u0947 \u0917\u090f \u0925\u0947\u0964 \u0909\u0926\u093e\u0939\u0930\u0923 \u0915\u0947 \u0932\u093f\u090f, \u090f\u0915 \u092a\u094d\u0930\u0936\u094d\u0928 \u092e\u0947\u0902 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0915\u0925\u0928\u094b\u0902 \u092e\u0947\u0902 \u0938\u0947 \u0915\u094c\u0928 \u0938\u093e \u0915\u0925\u0928 \u090f\u0915 \u0924\u093e\u0924\u094d\u0924\u094d\u0935\u093f\u0915 \u0938\u0924\u094d\u092f (tautology) \u0939\u0948, \u092f\u0939 \u092a\u0942\u091b\u093e \u0917\u092f\u093e \u0925\u093e:<\/p>\n<ol data-start=\"688\" data-end=\"897\">\n<li data-start=\"688\" data-end=\"754\"><span class=\"katex\"><span class=\"katex-mathml\">(P\u2192Q)\u2192(\u00acQ\u2192\u00acP)(P \\rightarrow Q) \\rightarrow (\\neg Q \\rightarrow \\neg P)<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">P<\/span><span class=\"mrel\">\u2192<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">Q<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">\u2192<\/span><\/span><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord\">\u00ac<\/span><span class=\"mord mathnormal\">Q<\/span><span class=\"mrel\">\u2192<\/span><\/span><span class=\"base\"><span class=\"mord\">\u00ac<\/span><span class=\"mord mathnormal\">P<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/li>\n<li data-start=\"755\" data-end=\"811\"><span class=\"katex\"><span class=\"katex-mathml\">(P\u2192Q)\u2192(Q\u2192P)(P \\rightarrow Q) \\rightarrow (Q \\rightarrow P)<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">P<\/span><span class=\"mrel\">\u2192<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">Q<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">\u2192<\/span><\/span><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">Q<\/span><span class=\"mrel\">\u2192<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">P<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/li>\n<li data-start=\"812\" data-end=\"852\"><span class=\"katex\"><span class=\"katex-mathml\">P\u2192(Q\u2192P)P \\rightarrow (Q \\rightarrow P)<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">P<\/span><span class=\"mrel\">\u2192<\/span><\/span><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">Q<\/span><span class=\"mrel\">\u2192<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">P<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/li>\n<li data-start=\"853\" data-end=\"897\"><span class=\"katex\"><span class=\"katex-mathml\">(P\u2227Q)\u2192(P\u2228Q)(P \\wedge Q) \\rightarrow (P \\vee Q)<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">P<\/span><span class=\"mbin\">\u2227<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">Q<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">\u2192<\/span><\/span><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">P<\/span><span class=\"mbin\">\u2228<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">Q<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/li>\n<\/ol>\n<p data-start=\"899\" data-end=\"910\"><strong data-start=\"899\" data-end=\"910\">\u0938\u092e\u093e\u0927\u093e\u0928:<\/strong><\/p>\n<ul data-start=\"912\" data-end=\"1478\">\n<li data-start=\"912\" data-end=\"1073\">\n<p data-start=\"914\" data-end=\"991\"><strong data-start=\"914\" data-end=\"927\">\u0935\u093f\u0915\u0932\u094d\u092a 1:<\/strong> <span class=\"katex\"><span class=\"katex-mathml\">(P\u2192Q)\u2192(\u00acQ\u2192\u00acP)(P \\rightarrow Q) \\rightarrow (\\neg Q \\rightarrow \\neg P)<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">P<\/span><span class=\"mrel\">\u2192<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">Q<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">\u2192<\/span><\/span><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord\">\u00ac<\/span><span class=\"mord mathnormal\">Q<\/span><span class=\"mrel\">\u2192<\/span><\/span><span class=\"base\"><span class=\"mord\">\u00ac<\/span><span class=\"mord mathnormal\">P<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/p>\n<ul data-start=\"994\" data-end=\"1073\">\n<li data-start=\"994\" data-end=\"1073\">\u092f\u0939 \u092a\u094d\u0930\u0924\u093f\u0932\u094b\u092e \u0928\u093f\u092f\u092e (Contrapositive Law) \u0915\u094b \u0926\u0930\u094d\u0936\u093e\u0924\u093e \u0939\u0948, \u091c\u094b \u090f\u0915 \u0924\u093e\u0924\u094d\u0924\u094d\u0935\u093f\u0915 \u0938\u0924\u094d\u092f \u0939\u0948\u0964<\/li>\n<\/ul>\n<\/li>\n<li data-start=\"1075\" data-end=\"1220\">\n<p data-start=\"1077\" data-end=\"1144\"><strong data-start=\"1077\" data-end=\"1090\">\u0935\u093f\u0915\u0932\u094d\u092a 2:<\/strong> <span class=\"katex\"><span class=\"katex-mathml\">(P\u2192Q)\u2192(Q\u2192P)(P \\rightarrow Q) \\rightarrow (Q \\rightarrow P)<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">P<\/span><span class=\"mrel\">\u2192<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">Q<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">\u2192<\/span><\/span><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">Q<\/span><span class=\"mrel\">\u2192<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">P<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/p>\n<ul data-start=\"1147\" data-end=\"1220\">\n<li data-start=\"1147\" data-end=\"1220\">\u092f\u0939 \u0915\u0925\u0928 \u0938\u092d\u0940 \u0938\u094d\u0925\u093f\u0924\u093f\u092f\u094b\u0902 \u092e\u0947\u0902 \u0938\u0924\u094d\u092f \u0928\u0939\u0940\u0902 \u0939\u0948, \u0907\u0938\u0932\u093f\u090f \u092f\u0939 \u0924\u093e\u0924\u094d\u0924\u094d\u0935\u093f\u0915 \u0938\u0924\u094d\u092f \u0928\u0939\u0940\u0902 \u0939\u0948\u0964<\/li>\n<\/ul>\n<\/li>\n<li data-start=\"1222\" data-end=\"1344\">\n<p data-start=\"1224\" data-end=\"1275\"><strong data-start=\"1224\" data-end=\"1237\">\u0935\u093f\u0915\u0932\u094d\u092a 3:<\/strong> <span class=\"katex\"><span class=\"katex-mathml\">P\u2192(Q\u2192P)P \\rightarrow (Q \\rightarrow P)<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">P<\/span><span class=\"mrel\">\u2192<\/span><\/span><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">Q<\/span><span class=\"mrel\">\u2192<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">P<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/p>\n<ul data-start=\"1278\" data-end=\"1344\">\n<li data-start=\"1278\" data-end=\"1344\">\u092f\u0939 \u0915\u0925\u0928 \u0938\u092d\u0940 \u0938\u094d\u0925\u093f\u0924\u093f\u092f\u094b\u0902 \u092e\u0947\u0902 \u0938\u0924\u094d\u092f \u0939\u0948, \u0907\u0938\u0932\u093f\u090f \u092f\u0939 \u090f\u0915 \u0924\u093e\u0924\u094d\u0924\u094d\u0935\u093f\u0915 \u0938\u0924\u094d\u092f \u0939\u0948\u0964<\/li>\n<\/ul>\n<\/li>\n<li data-start=\"1346\" data-end=\"1478\">\n<p data-start=\"1348\" data-end=\"1403\"><strong data-start=\"1348\" data-end=\"1361\">\u0935\u093f\u0915\u0932\u094d\u092a 4:<\/strong> <span class=\"katex\"><span class=\"katex-mathml\">(P\u2227Q)\u2192(P\u2228Q)(P \\wedge Q) \\rightarrow (P \\vee Q)<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">P<\/span><span class=\"mbin\">\u2227<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">Q<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">\u2192<\/span><\/span><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">P<\/span><span class=\"mbin\">\u2228<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">Q<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/p>\n<ul data-start=\"1406\" data-end=\"1478\">\n<li data-start=\"1406\" data-end=\"1478\">\u092f\u0939 \u0915\u0925\u0928 \u092d\u0940 \u0938\u092d\u0940 \u0938\u094d\u0925\u093f\u0924\u093f\u092f\u094b\u0902 \u092e\u0947\u0902 \u0938\u0924\u094d\u092f \u0939\u0948, \u0907\u0938\u0932\u093f\u090f \u092f\u0939 \u092d\u0940 \u090f\u0915 \u0924\u093e\u0924\u094d\u0924\u094d\u0935\u093f\u0915 \u0938\u0924\u094d\u092f \u0939\u0948\u0964<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p data-start=\"1480\" data-end=\"1746\">\u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930, \u0935\u093f\u0915\u0932\u094d\u092a 1, 3, \u0914\u0930 4 \u0924\u093e\u0924\u094d\u0924\u094d\u0935\u093f\u0915 \u0938\u0924\u094d\u092f \u0939\u0948\u0902\u0964 \u0939\u093e\u0932\u093e\u0902\u0915\u093f, \u092a\u094d\u0930\u0936\u094d\u0928 \u092e\u0947\u0902 \u0915\u0947\u0935\u0932 \u090f\u0915 \u0924\u093e\u0924\u094d\u0924\u094d\u0935\u093f\u0915 \u0938\u0924\u094d\u092f \u092a\u0942\u091b\u0940 \u0917\u0908 \u0939\u0948, \u0907\u0938\u0932\u093f\u090f \u092f\u0939 \u0938\u0902\u092d\u0935 \u0939\u0948 \u0915\u093f \u092a\u094d\u0930\u0936\u094d\u0928 \u092e\u0947\u0902 \u0924\u094d\u0930\u0941\u091f\u093f \u0939\u094b\u0964 \u0910\u0938\u0940 \u0938\u094d\u0925\u093f\u0924\u093f \u092e\u0947\u0902, \u0909\u092e\u094d\u092e\u0940\u0926\u0935\u093e\u0930\u094b\u0902 \u0915\u094b \u0906\u0927\u093f\u0915\u093e\u0930\u093f\u0915 \u0909\u0924\u094d\u0924\u0930 \u0915\u0941\u0902\u091c\u0940 \u092f\u093e \u092a\u0930\u0940\u0915\u094d\u0937\u093e \u092a\u094d\u0930\u093e\u0927\u093f\u0915\u0930\u0923 \u0926\u094d\u0935\u093e\u0930\u093e \u091c\u093e\u0930\u0940 \u0938\u094d\u092a\u0937\u094d\u091f\u0940\u0915\u0930\u0923 \u0915\u0940 \u092a\u094d\u0930\u0924\u0940\u0915\u094d\u0937\u093e \u0915\u0930\u0928\u0940 \u091a\u093e\u0939\u093f\u090f\u0964<\/p>\n<p data-start=\"1748\" data-end=\"1787\"><strong data-start=\"1748\" data-end=\"1787\">GATE 2025 \u0915\u0947 \u092a\u094d\u0930\u0936\u094d\u0928 \u092a\u0924\u094d\u0930 \u0939\u093f\u0902\u0926\u0940 \u092e\u0947\u0902:<\/strong><\/p>\n<p data-start=\"1789\" data-end=\"1907\">\u092f\u0926\u093f \u0906\u092a GATE 2025 \u0915\u0947 \u092a\u093f\u091b\u0932\u0947 \u0935\u0930\u094d\u0937 \u0915\u0947 \u092a\u094d\u0930\u0936\u094d\u0928 \u092a\u0924\u094d\u0930 \u0939\u093f\u0902\u0926\u0940 \u092e\u0947\u0902 \u0921\u093e\u0909\u0928\u0932\u094b\u0921 \u0915\u0930\u0928\u093e \u091a\u093e\u0939\u0924\u0947 \u0939\u0948\u0902, \u0924\u094b \u0906\u092a \u0906\u0927\u093f\u0915\u093e\u0930\u093f\u0915 \u0935\u0947\u092c\u0938\u093e\u0907\u091f \u092a\u0930 \u091c\u093e \u0938\u0915\u0924\u0947 \u0939\u0948\u0902:<\/p>\n<ul data-start=\"1909\" data-end=\"2004\">\n<li data-start=\"1909\" data-end=\"2004\">IIT \u0930\u0941\u0921\u093c\u0915\u0940 \u0926\u094d\u0935\u093e\u0930\u093e \u0906\u092f\u094b\u091c\u093f\u0924 GATE 2025 \u0915\u0940 \u0906\u0927\u093f\u0915\u093e\u0930\u093f\u0915 \u0935\u0947\u092c\u0938\u093e\u0907\u091f:<\/li>\n<\/ul>\n<p data-start=\"2006\" data-end=\"2126\">\u0907\u0938 \u0935\u0947\u092c\u0938\u093e\u0907\u091f \u092a\u0930, \u0906\u092a \u0935\u093f\u092d\u093f\u0928\u094d\u0928 \u0935\u093f\u0937\u092f\u094b\u0902 \u0915\u0947 \u092a\u094d\u0930\u0936\u094d\u0928 \u092a\u0924\u094d\u0930 \u0914\u0930 \u0909\u0928\u0915\u0947 \u0938\u092e\u093e\u0927\u093e\u0928 \u0921\u093e\u0909\u0928\u0932\u094b\u0921 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964 \u092f\u0939 \u0906\u092a\u0915\u0940 \u0924\u0948\u092f\u093e\u0930\u0940 \u092e\u0947\u0902 \u0938\u0939\u093e\u092f\u0915 \u0938\u093f\u0926\u094d\u0927 \u0939\u094b\u0917\u093e\u0964<\/p>\n<p data-start=\"2128\" data-end=\"2148\"><strong data-start=\"2128\" data-end=\"2148\">\u0924\u0948\u092f\u093e\u0930\u0940 \u0915\u0947 \u0938\u0941\u091d\u093e\u0935:<\/strong><\/p>\n<ul data-start=\"2150\" data-end=\"2358\">\n<li data-start=\"2150\" data-end=\"2244\">\u092a\u093f\u091b\u0932\u0947 \u0935\u0930\u094d\u0937\u094b\u0902 \u0915\u0947 \u092a\u094d\u0930\u0936\u094d\u0928 \u092a\u0924\u094d\u0930 \u0939\u0932 \u0915\u0930\u0947\u0902 \u0924\u093e\u0915\u093f \u092a\u0930\u0940\u0915\u094d\u0937\u093e \u092a\u0948\u091f\u0930\u094d\u0928 \u0914\u0930 \u092a\u094d\u0930\u0936\u094d\u0928\u094b\u0902 \u0915\u0947 \u092a\u094d\u0930\u0915\u093e\u0930 \u0915\u0940 \u0938\u092e\u091d \u0939\u094b \u0938\u0915\u0947\u0964<\/li>\n<li data-start=\"2245\" data-end=\"2304\">\u0924\u0941\u0932\u094d\u092f\u0924\u093e \u0914\u0930 \u0905\u0928\u094d\u092f \u0924\u093e\u0930\u094d\u0915\u093f\u0915 \u0905\u0935\u0927\u093e\u0930\u0923\u093e\u0913\u0902 \u0915\u0940 \u0917\u0939\u0928 \u0938\u092e\u091d \u0935\u093f\u0915\u0938\u093f\u0924 \u0915\u0930\u0947\u0902\u0964<\/li>\n<li data-start=\"2305\" data-end=\"2358\">\u092e\u0949\u0915 \u091f\u0947\u0938\u094d\u091f \u0926\u0947\u0902 \u0914\u0930 \u0905\u092a\u0928\u0940 \u0917\u0924\u093f \u0914\u0930 \u0938\u091f\u0940\u0915\u0924\u093e \u092e\u0947\u0902 \u0938\u0941\u0927\u093e\u0930 \u0915\u0930\u0947\u0902\u0964<\/li>\n<\/ul>\n<p data-start=\"2360\" data-end=\"2446\">\u0907\u0928 \u0938\u0941\u091d\u093e\u0935\u094b\u0902 \u0915\u093e \u092a\u093e\u0932\u0928 \u0915\u0930\u0915\u0947, \u0906\u092a GATE 2025 \u092e\u0947\u0902 \u0938\u092b\u0932 \u0939\u094b\u0928\u0947 \u0915\u0940 \u0905\u092a\u0928\u0940 \u0938\u0902\u092d\u093e\u0935\u0928\u093e\u0913\u0902 \u0915\u094b \u092c\u0922\u093c\u093e \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964<\/p>\n<h3 data-start=\"2360\" data-end=\"2446\"><a href=\"https:\/\/www2.cs.uh.edu\/~arjun\/courses\/ds\/DiscMaths4CompSc.pdf\" target=\"_blank\" rel=\"noopener\">Equivalence concept- GATE 2025 Discrete mathematics previous year paper in Hindi<\/a><\/h3>\n<h3 class=\"LC20lb MBeuO DKV0Md\"><a href=\"https:\/\/mrce.in\/ebooks\/Maths-Discrete%20Mathematics%20&amp;%20its%20Applications%208th%20Ed.pdf\" target=\"_blank\" rel=\"noopener\">Discrete Mathematics and Its Applications, Eighth Edition<\/a><\/h3>\n<p data-start=\"0\" data-end=\"112\"><span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\"><strong data-start=\"0\" data-end=\"13\" data-is-only-node=\"\">GATE 2025<\/strong> \u0915\u0940 \u0924\u0948\u092f\u093e\u0930\u0940 \u0915\u0930 \u0930\u0939\u0947 \u091b\u093e\u0924\u094d\u0930\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f, <strong data-start=\"47\" data-end=\"71\">Discrete Mathematics<\/strong> \u092e\u0947\u0902 <strong data-start=\"76\" data-end=\"115\">Equivalence Relation (\u0938\u092e\u093e\u0928\u0924\u093e \u0938\u0902\u092c\u0902\u0927)<\/strong> \u090f\u0915 \u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u0935\u093f\u0937\u092f \u0939\u0948\u0964<\/span> <span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\">\u092f\u0939\u093e\u0901 \u0939\u092e \u0907\u0938 \u0935\u093f\u0937\u092f \u0915\u0940 \u092e\u0942\u0932\u092d\u0942\u0924 \u0905\u0935\u0927\u093e\u0930\u0923\u093e\u0913\u0902, GATE \u092e\u0947\u0902 \u092a\u0942\u091b\u0947 \u0917\u090f \u092a\u093f\u091b\u0932\u0947 \u0935\u0930\u094d\u0937\u094b\u0902 \u0915\u0947 \u092a\u094d\u0930\u0936\u094d\u0928\u094b\u0902, \u0914\u0930 \u0909\u092a\u092f\u094b\u0917\u0940 \u0938\u0902\u0938\u093e\u0927\u0928\u094b\u0902 \u0915\u0947 \u092c\u093e\u0930\u0947 \u092e\u0947\u0902 \u091c\u093e\u0928\u0915\u093e\u0930\u0940 \u092a\u094d\u0930\u0926\u093e\u0928 \u0915\u0930 \u0930\u0939\u0947 \u0939\u0948\u0902\u0964<\/span><\/p>\n<hr data-start=\"114\" data-end=\"117\" \/>\n<h2 data-start=\"119\" data-end=\"169\">\ud83d\udcd8 <strong data-start=\"125\" data-end=\"169\">Equivalence Relation \u0915\u0940 \u092e\u0942\u0932\u092d\u0942\u0924 \u0905\u0935\u0927\u093e\u0930\u0923\u093e\u090f\u0901<\/strong><\/h2>\n<p data-start=\"171\" data-end=\"247\"><span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\">\u090f\u0915 <strong data-start=\"3\" data-end=\"27\">Equivalence Relation<\/strong> \u0935\u0939 \u092c\u093e\u0907\u0928\u0930\u0940 \u0938\u0902\u092c\u0902\u0927 \u0939\u094b\u0924\u093e \u0939\u0948 \u091c\u094b \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0924\u0940\u0928 \u0917\u0941\u0923\u094b\u0902 \u0915\u094b \u0938\u0902\u0924\u0941\u0937\u094d\u091f \u0915\u0930\u0924\u093e \u0939\u0948:<\/span><\/p>\n<ol data-start=\"249\" data-end=\"501\">\n<li data-start=\"249\" data-end=\"321\">\n<p data-start=\"252\" data-end=\"321\"><strong data-start=\"252\" data-end=\"281\">Reflexive (\u092a\u0930\u093e\u0935\u0930\u094d\u0924\u0928\u0940\u092f\u0924\u093e):<\/strong> <span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\">\u0939\u0930 \u0924\u0924\u094d\u0935 \u0938\u094d\u0935\u092f\u0902 \u0938\u0947 \u0938\u0902\u092c\u0902\u0927\u093f\u0924 \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u0909\u0926\u093e\u0939\u0930\u0923: \u2200a \u2208 A, (a, a) \u2208 R<\/span><\/p>\n<\/li>\n<li data-start=\"322\" data-end=\"389\">\n<p data-start=\"325\" data-end=\"389\"><strong data-start=\"325\" data-end=\"349\">Symmetric (\u0938\u092e\u092e\u093f\u0924\u0924\u093e):<\/strong> <span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\">\u092f\u0926\u093f a \u0915\u093f\u0938\u0940 b \u0938\u0947 \u0938\u0902\u092c\u0902\u0927\u093f\u0924 \u0939\u0948, \u0924\u094b b \u092d\u0940 a \u0938\u0947 \u0938\u0902\u092c\u0902\u0927\u093f\u0924 \u0939\u094b\u0917\u093e\u0964 \u0909\u0926\u093e\u0939\u0930\u0923: \u092f\u0926\u093f (a, b) \u2208 R, \u0924\u094b (b, a) \u2208 R<\/span><\/p>\n<\/li>\n<li data-start=\"390\" data-end=\"501\">\n<p data-start=\"393\" data-end=\"501\"><strong data-start=\"393\" data-end=\"422\">Transitive (\u0938\u093e\u0902\u0915\u094d\u0930\u093e\u092e\u0915\u0924\u093e):<\/strong> <span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\">\u092f\u0926\u093f a \u0915\u093f\u0938\u0940 b \u0938\u0947 \u0914\u0930 b \u0915\u093f\u0938\u0940 c \u0938\u0947 \u0938\u0902\u092c\u0902\u0927\u093f\u0924 \u0939\u0948, \u0924\u094b a \u092d\u0940 c \u0938\u0947 \u0938\u0902\u092c\u0902\u0927\u093f\u0924 \u0939\u094b\u0917\u093e\u0964 \u0909\u0926\u093e\u0939\u0930\u0923: \u092f\u0926\u093f (a, b) \u2208 R \u0914\u0930 (b, c) \u2208 R, \u0924\u094b (a, c) \u2208 R<\/span><\/p>\n<\/li>\n<\/ol>\n<p data-start=\"503\" data-end=\"581\"><span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\">\u092f\u0926\u093f \u0915\u094b\u0908 \u0938\u0902\u092c\u0902\u0927 \u0907\u0928 \u0924\u0940\u0928\u094b\u0902 \u0917\u0941\u0923\u094b\u0902 \u0915\u094b \u0938\u0902\u0924\u0941\u0937\u094d\u091f \u0915\u0930\u0924\u093e \u0939\u0948, \u0924\u094b \u0935\u0939 <strong data-start=\"55\" data-end=\"79\">Equivalence Relation<\/strong> \u0915\u0939\u0932\u093e\u0924\u093e \u0939\u0948\u0964<\/span><\/p>\n<hr data-start=\"583\" data-end=\"586\" \/>\n<h2 data-start=\"588\" data-end=\"653\">\ud83d\udcda <strong data-start=\"594\" data-end=\"653\">GATE \u092e\u0947\u0902 \u092a\u0942\u091b\u0947 \u0917\u090f Equivalence Relation \u0938\u0947 \u0938\u0902\u092c\u0902\u0927\u093f\u0924 \u092a\u094d\u0930\u0936\u094d\u0928<\/strong><\/h2>\n<p data-start=\"655\" data-end=\"733\"><span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\">GATE \u092a\u0930\u0940\u0915\u094d\u0937\u093e \u092e\u0947\u0902 Equivalence Relation \u0938\u0947 \u0938\u0902\u092c\u0902\u0927\u093f\u0924 \u0915\u0908 \u092a\u094d\u0930\u0936\u094d\u0928 \u092a\u0942\u091b\u0947 \u0917\u090f \u0939\u0948\u0902\u0964 \u0909\u0926\u093e\u0939\u0930\u0923 \u0915\u0947 \u0932\u093f\u090f:<\/span><\/p>\n<p data-start=\"735\" data-end=\"825\"><strong data-start=\"735\" data-end=\"746\">\u092a\u094d\u0930\u0936\u094d\u0928:<\/strong> <span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\">\u092f\u0926\u093f \u0915\u094b\u0908 \u0938\u0902\u092c\u0902\u0927 R \u0938\u0947\u091f A \u092a\u0930 \u092a\u0930\u093e\u0935\u0930\u094d\u0924\u0928\u0940\u092f \u0914\u0930 \u0938\u092e\u092e\u093f\u0924 \u0939\u0948, \u0924\u094b \u0915\u094d\u092f\u093e R \u0906\u0935\u0936\u094d\u092f\u0915 \u0930\u0942\u092a \u0938\u0947 Equivalence Relation \u0939\u094b\u0917\u093e?<\/span><\/p>\n<p data-start=\"827\" data-end=\"916\"><strong data-start=\"827\" data-end=\"837\">\u0909\u0924\u094d\u0924\u0930:<\/strong> <span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\">\u0928\u0939\u0940\u0902, \u0915\u094d\u092f\u094b\u0902\u0915\u093f Equivalence Relation \u0915\u0947 \u0932\u093f\u090f \u091f\u094d\u0930\u093e\u0902\u091c\u093f\u091f\u093f\u0935 \u0939\u094b\u0928\u093e \u092d\u0940 \u0906\u0935\u0936\u094d\u092f\u0915 \u0939\u0948\u0964<\/span><\/p>\n<p data-start=\"918\" data-end=\"996\"><span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\">\u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0915\u0947 \u0914\u0930 \u092a\u094d\u0930\u0936\u094d\u0928\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f, \u0906\u092a \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0938\u0902\u0938\u093e\u0927\u0928\u094b\u0902 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902:<\/span><\/p>\n<ul data-start=\"998\" data-end=\"1238\">\n<li data-start=\"998\" data-end=\"1098\">\n<p data-start=\"1000\" data-end=\"1098\"><strong data-start=\"1000\" data-end=\"1018\">GeeksforGeeks:<\/strong> <span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\">\u092f\u0939\u093e\u0901 \u092a\u0930 Discrete Mathematics \u0915\u0947 GATE \u0915\u0947 \u092a\u093f\u091b\u0932\u0947 \u0935\u0930\u094d\u0937\u094b\u0902 \u0915\u0947 \u092a\u094d\u0930\u0936\u094d\u0928 \u0909\u092a\u0932\u092c\u094d\u0927 \u0939\u0948\u0902\u0964<\/span><\/p>\n<\/li>\n<li data-start=\"1099\" data-end=\"1238\">\n<p data-start=\"1101\" data-end=\"1238\"><strong data-start=\"1101\" data-end=\"1119\">PracticePaper:<\/strong> <span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\">\u092f\u0939 \u0938\u093e\u0907\u091f Relation \u0938\u0947 \u0938\u0902\u092c\u0902\u0927\u093f\u0924 GATE CSE \u0915\u0947 \u092a\u093f\u091b\u0932\u0947 \u0935\u0930\u094d\u0937\u094b\u0902 \u0915\u0947 \u092a\u094d\u0930\u0936\u094d\u0928\u094b\u0902 \u0915\u093e \u0905\u092d\u094d\u092f\u093e\u0938 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0909\u092a\u092f\u0941\u0915\u094d\u0924 \u0939\u0948\u0964<\/span><\/p>\n<\/li>\n<\/ul>\n<hr data-start=\"1240\" data-end=\"1243\" \/>\n<h2 data-start=\"1245\" data-end=\"1278\">\ud83c\udfa5 <strong data-start=\"1251\" data-end=\"1278\">\u0939\u093f\u0902\u0926\u0940 \u092e\u0947\u0902 \u0935\u0940\u0921\u093f\u092f\u094b \u0938\u0902\u0938\u093e\u0927\u0928<\/strong><\/h2>\n<p data-start=\"1280\" data-end=\"1358\"><span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\">Equivalence Relation \u0915\u0940 \u092c\u0947\u0939\u0924\u0930 \u0938\u092e\u091d \u0915\u0947 \u0932\u093f\u090f, \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0939\u093f\u0902\u0926\u0940 \u0935\u0940\u0921\u093f\u092f\u094b \u0932\u0947\u0915\u094d\u091a\u0930 \u0938\u0939\u093e\u092f\u0915 \u0939\u094b \u0938\u0915\u0924\u0947 \u0939\u0948\u0902:<\/span><\/p>\n<ul data-start=\"1360\" data-end=\"1679\">\n<li data-start=\"1360\" data-end=\"1508\">\n<p data-start=\"1362\" data-end=\"1508\"><strong data-start=\"1362\" data-end=\"1428\">Equivalence Relation | Discrete Mathematics Lectures in Hindi:<\/strong> <span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\">\u0907\u0938 \u0935\u0940\u0921\u093f\u092f\u094b \u092e\u0947\u0902 Equivalence Relation \u0915\u0940 \u0905\u0935\u0927\u093e\u0930\u0923\u093e\u0913\u0902 \u0915\u094b \u0935\u093f\u0938\u094d\u0924\u093e\u0930 \u0938\u0947 \u0938\u092e\u091d\u093e\u092f\u093e \u0917\u092f\u093e \u0939\u0948\u0964<\/span><\/p>\n<\/li>\n<li data-start=\"1509\" data-end=\"1679\">\n<p data-start=\"1511\" data-end=\"1679\"><strong data-start=\"1511\" data-end=\"1560\">Equivalence Relation (GATE Problems) &#8211; Set 1:<\/strong> <span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\">\u092f\u0939 \u0935\u0940\u0921\u093f\u092f\u094b GATE \u092a\u0930\u0940\u0915\u094d\u0937\u093e \u092e\u0947\u0902 \u092a\u0942\u091b\u0947 \u0917\u090f Equivalence Relation \u0938\u0947 \u0938\u0902\u092c\u0902\u0927\u093f\u0924 \u092a\u094d\u0930\u0936\u094d\u0928\u094b\u0902 \u092a\u0930 \u0915\u0947\u0902\u0926\u094d\u0930\u093f\u0924 \u0939\u0948\u0964<\/span><\/p>\n<\/li>\n<\/ul>\n<hr data-start=\"1681\" data-end=\"1684\" \/>\n<h2 data-start=\"1686\" data-end=\"1715\">\ud83e\udde0 <strong data-start=\"1692\" data-end=\"1715\">\u0905\u092d\u094d\u092f\u093e\u0938 \u0915\u0947 \u0932\u093f\u090f \u0938\u0941\u091d\u093e\u0935<\/strong><\/h2>\n<ul data-start=\"1717\" data-end=\"1950\">\n<li data-start=\"1717\" data-end=\"1788\">\n<p data-start=\"1719\" data-end=\"1788\"><strong data-start=\"1719\" data-end=\"1748\">\u0938\u0924\u094d\u092f \u0938\u093e\u0930\u0923\u0940 (Truth Table):<\/strong> <span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\">Equivalence Relation \u0915\u0947 \u0917\u0941\u0923\u094b\u0902 \u0915\u094b \u0938\u0924\u094d\u092f\u093e\u092a\u093f\u0924 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0938\u0924\u094d\u092f \u0938\u093e\u0930\u0923\u0940 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0947\u0902\u0964<\/span><\/p>\n<\/li>\n<li data-start=\"1789\" data-end=\"1854\">\n<p data-start=\"1791\" data-end=\"1854\"><strong data-start=\"1791\" data-end=\"1814\">\u0909\u0926\u093e\u0939\u0930\u0923\u094b\u0902 \u0915\u093e \u0905\u092d\u094d\u092f\u093e\u0938:<\/strong> <span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\">\u0935\u093f\u092d\u093f\u0928\u094d\u0928 \u0938\u0947\u091f\u094d\u0938 \u0914\u0930 \u0938\u0902\u092c\u0902\u0927\u094b\u0902 \u0915\u0947 \u0909\u0926\u093e\u0939\u0930\u0923\u094b\u0902 \u092a\u0930 \u0905\u092d\u094d\u092f\u093e\u0938 \u0915\u0930\u0947\u0902 \u0924\u093e\u0915\u093f \u0905\u0935\u0927\u093e\u0930\u0923\u093e\u090f\u0901 \u0938\u094d\u092a\u0937\u094d\u091f \u0939\u094b\u0902\u0964<\/span><\/p>\n<\/li>\n<li data-start=\"1855\" data-end=\"1950\">\n<p data-start=\"1857\" data-end=\"1950\"><strong data-start=\"1857\" data-end=\"1871\">\u092e\u0949\u0915 \u091f\u0947\u0938\u094d\u091f:<\/strong> <span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem] transition-colors duration-100 ease-in-out\">GATE \u0915\u0947 \u092a\u093f\u091b\u0932\u0947 \u0935\u0930\u094d\u0937\u094b\u0902 \u0915\u0947 \u092a\u094d\u0930\u0936\u094d\u0928\u094b\u0902 \u0915\u093e \u0905\u092d\u094d\u092f\u093e\u0938 \u0915\u0930\u0947\u0902 \u0924\u093e\u0915\u093f \u092a\u0930\u0940\u0915\u094d\u0937\u093e \u092a\u0948\u091f\u0930\u094d\u0928 \u0915\u0940 \u0938\u092e\u091d \u0935\u093f\u0915\u0938\u093f\u0924 \u0939\u094b\u0964<\/span><\/p>\n<\/li>\n<\/ul>\n<hr data-start=\"1952\" data-end=\"1955\" \/>\n<p data-start=\"1957\" data-end=\"2066\">\u092f\u0926\u093f \u0906\u092a \u0915\u093f\u0938\u0940 \u0935\u093f\u0936\u0947\u0937 \u092a\u094d\u0930\u0936\u094d\u0928 \u092f\u093e \u0905\u0935\u0927\u093e\u0930\u0923\u093e \u092a\u0930 \u0914\u0930 \u091c\u093e\u0928\u0915\u093e\u0930\u0940 \u091a\u093e\u0939\u0924\u0947 \u0939\u0948\u0902, \u0924\u094b \u0915\u0943\u092a\u092f\u093e \u092c\u0924\u093e\u090f\u0902\u0964 \u092e\u0948\u0902 \u0906\u092a\u0915\u0940 \u0938\u0939\u093e\u092f\u0924\u093e \u0915\u0947 \u0932\u093f\u090f \u092f\u0939\u093e\u0901 \u0939\u0942\u0901!<\/p>\n<h3 data-start=\"1957\" data-end=\"2066\"><a href=\"https:\/\/www.vidyalankar.org\/gate\/assets\/docs\/notes\/maths.pdf\" target=\"_blank\" rel=\"noopener\">Equivalence concept- GATE 2025 Discrete mathematics previous year paper in Hindi<\/a><\/h3>\n<h3 class=\"LC20lb MBeuO DKV0Md\"><a href=\"https:\/\/www.aicte-india.org\/sites\/default\/files\/MQP.pdf\" target=\"_blank\" rel=\"noopener\">Model Question Papers<\/a><\/h3>\n","protected":false},"excerpt":{"rendered":"<p>Equivalence concept- GATE 2025 Discrete mathematics previous year paper in Hindi [fvplayer id=&#8221;179&#8243;] \u0924\u0941\u0932\u094d\u092f\u0924\u093e (Equivalence) \u0924\u093e\u0930\u094d\u0915\u093f\u0915 \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, \u091c\u094b \u0926\u094b \u0915\u0925\u0928\u094b\u0902 \u092f\u093e \u0938\u0942\u0924\u094d\u0930\u094b\u0902 \u0915\u0947 \u0938\u092e\u093e\u0928 \u0938\u0924\u094d\u092f-\u092e\u0942\u0932\u094d\u092f \u0915\u094b \u0928\u093f\u0930\u0942\u092a\u093f\u0924 \u0915\u0930\u0924\u0940 \u0939\u0948\u0964 \u092f\u0926\u093f \u0926\u094b \u0924\u093e\u0930\u094d\u0915\u093f\u0915 \u0915\u0925\u0928 \u0938\u092d\u0940 \u0938\u0902\u092d\u093e\u0935\u093f\u0924 \u0938\u094d\u0925\u093f\u0924\u093f\u092f\u094b\u0902 \u092e\u0947\u0902 \u0938\u092e\u093e\u0928 \u0938\u0924\u094d\u092f-\u092e\u0942\u0932\u094d\u092f \u0930\u0916\u0924\u0947 \u0939\u0948\u0902, \u0924\u094b \u0935\u0947 \u0924\u0941\u0932\u094d\u092f \u0915\u0939\u0932\u093e\u0924\u0947 \u0939\u0948\u0902\u0964 \u0909\u0926\u093e\u0939\u0930\u0923 \u0915\u0947 \u0932\u093f\u090f, \u0915\u0925\u0928 [&hellip;]<\/p>\n","protected":false},"author":71,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[76],"tags":[],"class_list":["post-2938","post","type-post","status-publish","format-standard","hentry","category-discrete-mathematics"],"_links":{"self":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts\/2938","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/users\/71"}],"replies":[{"embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/comments?post=2938"}],"version-history":[{"count":0,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts\/2938\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/media?parent=2938"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/categories?post=2938"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/tags?post=2938"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}