{"id":3033,"date":"2025-06-07T14:20:45","date_gmt":"2025-06-07T14:20:45","guid":{"rendered":"https:\/\/diznr.com\/?p=3033"},"modified":"2025-06-07T14:20:45","modified_gmt":"2025-06-07T14:20:45","slug":"day-03part-06-discrete-mathematics-in-hindi-concept-of-maximal-and-minimal-with-maximum-minimum-and","status":"publish","type":"post","link":"https:\/\/www.reilsolar.com\/pdf\/day-03part-06-discrete-mathematics-in-hindi-concept-of-maximal-and-minimal-with-maximum-minimum-and\/","title":{"rendered":"Day 03Part 06-Discrete Mathematics in Hindi-Concept of maximal and minimal with maximum and minimum."},"content":{"rendered":"<p>Day 03Part 06-Discrete Mathematics in Hindi-Concept of maximal and minimal with maximum and minimum.<\/p>\n<p>[fvplayer id=&#8221;225&#8243;]<\/p>\n<p class=\"\" data-start=\"0\" data-end=\"126\">\u200b<span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem]\">\u0921\u093f\u0938\u094d\u0915\u094d\u0930\u0940\u091f \u0917\u0923\u093f\u0924 \u092e\u0947\u0902, <strong data-start=\"20\" data-end=\"63\">\u092e\u0948\u0915\u094d\u0938\u093f\u092e\u0932 (\u0938\u0930\u094d\u0935\u094b\u091a\u094d\u091a) \u0914\u0930 \u092e\u093f\u0928\u093f\u092e\u0932 (\u0928\u094d\u092f\u0942\u0928\u0924\u092e)<\/strong> \u0924\u0924\u094d\u0935\u094b\u0902 \u0915\u0940 \u0905\u0935\u0927\u093e\u0930\u0923\u093e \u0906\u0902\u0936\u093f\u0915 \u0915\u094d\u0930\u092e\u093f\u0924 \u0938\u092e\u0941\u091a\u094d\u091a\u092f\u094b\u0902 (partially ordered sets) \u092e\u0947\u0902 \u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u092d\u0942\u092e\u093f\u0915\u093e \u0928\u093f\u092d\u093e\u0924\u0940 \u0939\u0948\u0964<\/span> <span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem]\">\u0907\u0928 \u0905\u0935\u0927\u093e\u0930\u0923\u093e\u0913\u0902 \u0915\u094b \u0938\u092e\u091d\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f, \u0939\u092e\u0947\u0902 \u092a\u0939\u0932\u0947 \u0906\u0902\u0936\u093f\u0915 \u0915\u094d\u0930\u092e \u0914\u0930 \u0906\u0902\u0936\u093f\u0915 \u0915\u094d\u0930\u092e\u093f\u0924 \u0938\u092e\u0941\u091a\u094d\u091a\u092f \u0915\u0940 \u0938\u092e\u091d \u0939\u094b\u0928\u0940 \u091a\u093e\u0939\u093f\u090f\u0964<\/span>\u200b<\/p>\n<p class=\"\" data-start=\"128\" data-end=\"177\"><strong data-start=\"128\" data-end=\"177\">\u0906\u0902\u0936\u093f\u0915 \u0915\u094d\u0930\u092e\u093f\u0924 \u0938\u092e\u0941\u091a\u094d\u091a\u092f (Partially Ordered Set):<\/strong><\/p>\n<p class=\"\" data-start=\"179\" data-end=\"260\"><span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem]\">\u092f\u0926\u093f \u090f\u0915 \u0938\u092e\u0941\u091a\u094d\u091a\u092f <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> \u092a\u0930 \u090f\u0915 \u0926\u094d\u0935\u093f\u091a\u0930 \u0938\u0902\u092c\u0902\u0927 <span class=\"katex\"><span class=\"katex-mathml\">\u2264\\leq<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mrel\">\u2264<\/span><\/span><\/span><\/span> \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0915\u093f\u092f\u093e \u0917\u092f\u093e \u0939\u0948 \u0915\u093f:<\/span>\u200b<\/p>\n<ol data-start=\"262\" data-end=\"614\">\n<li class=\"\" data-start=\"262\" data-end=\"378\">\n<p class=\"\" data-start=\"265\" data-end=\"378\"><strong data-start=\"265\" data-end=\"296\">\u092a\u094d\u0930\u0924\u093f\u0935\u0930\u094d\u0924\u0940\u0924\u093e (Reflexivity):<\/strong> <span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem]\">\u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 <span class=\"katex\"><span class=\"katex-mathml\">a\u2208Pa \\in P<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">a<\/span><span class=\"mrel\">\u2208<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">P<\/span><\/span><\/span><\/span> \u0915\u0947 \u0932\u093f\u090f, <span class=\"katex\"><span class=\"katex-mathml\">a\u2264aa \\leq a<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">a<\/span><span class=\"mrel\">\u2264<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">a<\/span><\/span><\/span><\/span>\u0964<\/span>\u200b<\/p>\n<\/li>\n<li class=\"\" data-start=\"379\" data-end=\"495\">\n<p class=\"\" data-start=\"382\" data-end=\"495\"><strong data-start=\"382\" data-end=\"413\">\u092a\u093e\u0930\u0938\u094d\u092a\u0930\u093f\u0915\u0924\u093e (Antisymmetry):<\/strong> <span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem]\">\u092f\u0926\u093f <span class=\"katex\"><span class=\"katex-mathml\">a\u2264ba \\leq b<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">a<\/span><span class=\"mrel\">\u2264<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">b<\/span><\/span><\/span><\/span> \u0914\u0930 <span class=\"katex\"><span class=\"katex-mathml\">b\u2264ab \\leq a<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">b<\/span><span class=\"mrel\">\u2264<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">a<\/span><\/span><\/span><\/span>, \u0924\u094b <span class=\"katex\"><span class=\"katex-mathml\">a=ba = b<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">a<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">b<\/span><\/span><\/span><\/span>\u0964<\/span>\u200b<\/p>\n<\/li>\n<li class=\"\" data-start=\"496\" data-end=\"614\">\n<p class=\"\" data-start=\"499\" data-end=\"614\"><strong data-start=\"499\" data-end=\"530\">\u0938\u093e\u0902\u0915\u094d\u0930\u092e\u093f\u0915\u0924\u093e (Transitivity):<\/strong> <span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem]\">\u092f\u0926\u093f <span class=\"katex\"><span class=\"katex-mathml\">a\u2264ba \\leq b<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">a<\/span><span class=\"mrel\">\u2264<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">b<\/span><\/span><\/span><\/span> \u0914\u0930 <span class=\"katex\"><span class=\"katex-mathml\">b\u2264cb \\leq c<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">b<\/span><span class=\"mrel\">\u2264<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">c<\/span><\/span><\/span><\/span>, \u0924\u094b <span class=\"katex\"><span class=\"katex-mathml\">a\u2264ca \\leq c<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">a<\/span><span class=\"mrel\">\u2264<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">c<\/span><\/span><\/span><\/span>\u0964<\/span>\u200b<\/p>\n<\/li>\n<\/ol>\n<p class=\"\" data-start=\"616\" data-end=\"701\"><span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem]\">\u0924\u094b <span class=\"katex\"><span class=\"katex-mathml\">(P,\u2264)(P, \\leq)<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">P<\/span><span class=\"mpunct\">,<\/span><span class=\"mrel\">\u2264<\/span><\/span><span class=\"base\"><span class=\"mclose\">)<\/span><\/span><\/span><\/span> \u090f\u0915 \u0906\u0902\u0936\u093f\u0915 \u0915\u094d\u0930\u092e\u093f\u0924 \u0938\u092e\u0941\u091a\u094d\u091a\u092f \u0915\u0939\u0932\u093e\u0924\u093e \u0939\u0948\u0964<\/span>\u200b<\/p>\n<p class=\"\" data-start=\"703\" data-end=\"731\"><strong data-start=\"703\" data-end=\"731\">\u092e\u0948\u0915\u094d\u0938\u093f\u092e\u0932 \u0914\u0930 \u092e\u093f\u0928\u093f\u092e\u0932 \u0924\u0924\u094d\u0935:<\/strong><\/p>\n<ul data-start=\"733\" data-end=\"981\">\n<li class=\"\" data-start=\"733\" data-end=\"857\">\n<p class=\"\" data-start=\"735\" data-end=\"857\"><strong data-start=\"735\" data-end=\"771\">\u092e\u0948\u0915\u094d\u0938\u093f\u092e\u0932 \u0924\u0924\u094d\u0935 (Maximal Element):<\/strong> <span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem]\">\u0938\u092e\u0941\u091a\u094d\u091a\u092f <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> \u0915\u093e \u090f\u0915 \u0924\u0924\u094d\u0935 <span class=\"katex\"><span class=\"katex-mathml\">mm<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">m<\/span><\/span><\/span><\/span> \u092e\u0948\u0915\u094d\u0938\u093f\u092e\u0932 \u0915\u0939\u0932\u093e\u0924\u093e \u0939\u0948 \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> \u092e\u0947\u0902 \u0915\u094b\u0908 \u092d\u0940 \u0905\u0928\u094d\u092f \u0924\u0924\u094d\u0935 <span class=\"katex\"><span class=\"katex-mathml\">xx<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span> \u0910\u0938\u093e \u0928\u0939\u0940\u0902 \u0939\u0948 \u0915\u093f <span class=\"katex\"><span class=\"katex-mathml\">m\u2264xm \\leq x<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">m<\/span><span class=\"mrel\">\u2264<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span> \u0914\u0930 <span class=\"katex\"><span class=\"katex-mathml\">m\u2260xm \\neq x<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">m<\/span><span class=\"mrel\"><span class=\"mord vbox\"><span class=\"thinbox\"><span class=\"rlap\"><span class=\"inner\"><span class=\"mord\">\ue020<\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span>\u0964 \u0938\u0930\u0932 \u0936\u092c\u094d\u0926\u094b\u0902 \u092e\u0947\u0902, <span class=\"katex\"><span class=\"katex-mathml\">mm<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">m<\/span><\/span><\/span><\/span> \u0915\u0947 \u092c\u093e\u0926 \u0915\u094b\u0908 \u0905\u0928\u094d\u092f \u092c\u0921\u093c\u093e \u0924\u0924\u094d\u0935 \u0928\u0939\u0940\u0902 \u0939\u0948\u0964<\/span>\u200b<\/p>\n<\/li>\n<li class=\"\" data-start=\"859\" data-end=\"981\">\n<p class=\"\" data-start=\"861\" data-end=\"981\"><strong data-start=\"861\" data-end=\"895\">\u092e\u093f\u0928\u093f\u092e\u0932 \u0924\u0924\u094d\u0935 (Minimal Element):<\/strong> <span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem]\">\u0938\u092e\u0941\u091a\u094d\u091a\u092f <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> \u0915\u093e \u090f\u0915 \u0924\u0924\u094d\u0935 <span class=\"katex\"><span class=\"katex-mathml\">nn<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">n<\/span><\/span><\/span><\/span> \u092e\u093f\u0928\u093f\u092e\u0932 \u0915\u0939\u0932\u093e\u0924\u093e \u0939\u0948 \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> \u092e\u0947\u0902 \u0915\u094b\u0908 \u092d\u0940 \u0905\u0928\u094d\u092f \u0924\u0924\u094d\u0935 <span class=\"katex\"><span class=\"katex-mathml\">xx<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span> \u0910\u0938\u093e \u0928\u0939\u0940\u0902 \u0939\u0948 \u0915\u093f <span class=\"katex\"><span class=\"katex-mathml\">x\u2264nx \\leq n<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">x<\/span><span class=\"mrel\">\u2264<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">n<\/span><\/span><\/span><\/span> \u0914\u0930 <span class=\"katex\"><span class=\"katex-mathml\">n\u2260xn \\neq x<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">n<\/span><span class=\"mrel\"><span class=\"mord vbox\"><span class=\"thinbox\"><span class=\"rlap\"><span class=\"inner\"><span class=\"mord\">\ue020<\/span><\/span><\/span><\/span><\/span>=<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span>\u0964 \u0905\u0930\u094d\u0925\u093e\u0924, <span class=\"katex\"><span class=\"katex-mathml\">nn<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">n<\/span><\/span><\/span><\/span> \u0938\u0947 \u092a\u0939\u0932\u0947 \u0915\u094b\u0908 \u0905\u0928\u094d\u092f \u091b\u094b\u091f\u093e \u0924\u0924\u094d\u0935 \u0928\u0939\u0940\u0902 \u0939\u0948\u0964<\/span>\u200b<\/p>\n<\/li>\n<\/ul>\n<p class=\"\" data-start=\"983\" data-end=\"1011\"><strong data-start=\"983\" data-end=\"1011\">\u092e\u0948\u0915\u094d\u0938\u093f\u092e\u092e \u0914\u0930 \u092e\u093f\u0928\u093f\u092e\u092e \u0924\u0924\u094d\u0935:<\/strong><\/p>\n<ul data-start=\"1013\" data-end=\"1261\">\n<li class=\"\" data-start=\"1013\" data-end=\"1137\">\n<p class=\"\" data-start=\"1015\" data-end=\"1137\"><strong data-start=\"1015\" data-end=\"1051\">\u092e\u0948\u0915\u094d\u0938\u093f\u092e\u092e \u0924\u0924\u094d\u0935 (Maximum Element):<\/strong> <span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem]\">\u092f\u0926\u093f \u0938\u092e\u0941\u091a\u094d\u091a\u092f <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> \u092e\u0947\u0902 \u090f\u0915 \u0910\u0938\u093e \u0924\u0924\u094d\u0935 <span class=\"katex\"><span class=\"katex-mathml\">MM<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">M<\/span><\/span><\/span><\/span> \u0939\u0948 \u091c\u094b \u0938\u092d\u0940 \u0924\u0924\u094d\u0935\u094b\u0902 \u0938\u0947 \u092c\u0921\u093c\u093e \u0939\u0948, \u0905\u0930\u094d\u0925\u093e\u0924 \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 <span class=\"katex\"><span class=\"katex-mathml\">x\u2208Px \\in P<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">x<\/span><span class=\"mrel\">\u2208<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">P<\/span><\/span><\/span><\/span> \u0915\u0947 \u0932\u093f\u090f <span class=\"katex\"><span class=\"katex-mathml\">x\u2264Mx \\leq M<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">x<\/span><span class=\"mrel\">\u2264<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">M<\/span><\/span><\/span><\/span>, \u0924\u094b <span class=\"katex\"><span class=\"katex-mathml\">MM<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">M<\/span><\/span><\/span><\/span> \u092e\u0948\u0915\u094d\u0938\u093f\u092e\u092e \u0924\u0924\u094d\u0935 \u0915\u0939\u0932\u093e\u0924\u093e \u0939\u0948\u0964<\/span>\u200b<\/p>\n<\/li>\n<li class=\"\" data-start=\"1139\" data-end=\"1261\">\n<p class=\"\" data-start=\"1141\" data-end=\"1261\"><strong data-start=\"1141\" data-end=\"1175\">\u092e\u093f\u0928\u093f\u092e\u092e \u0924\u0924\u094d\u0935 (Minimum Element):<\/strong> <span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem]\">\u092f\u0926\u093f \u0938\u092e\u0941\u091a\u094d\u091a\u092f <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> \u092e\u0947\u0902 \u090f\u0915 \u0910\u0938\u093e \u0924\u0924\u094d\u0935 <span class=\"katex\"><span class=\"katex-mathml\">mm<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">m<\/span><\/span><\/span><\/span> \u0939\u0948 \u091c\u094b \u0938\u092d\u0940 \u0924\u0924\u094d\u0935\u094b\u0902 \u0938\u0947 \u091b\u094b\u091f\u093e \u0939\u0948, \u0905\u0930\u094d\u0925\u093e\u0924 \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 <span class=\"katex\"><span class=\"katex-mathml\">x\u2208Px \\in P<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">x<\/span><span class=\"mrel\">\u2208<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">P<\/span><\/span><\/span><\/span> \u0915\u0947 \u0932\u093f\u090f <span class=\"katex\"><span class=\"katex-mathml\">m\u2264xm \\leq x<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">m<\/span><span class=\"mrel\">\u2264<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">x<\/span><\/span><\/span><\/span>, \u0924\u094b <span class=\"katex\"><span class=\"katex-mathml\">mm<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">m<\/span><\/span><\/span><\/span> \u092e\u093f\u0928\u093f\u092e\u092e \u0924\u0924\u094d\u0935 \u0915\u0939\u0932\u093e\u0924\u093e \u0939\u0948\u0964<\/span>\u200b<\/p>\n<\/li>\n<\/ul>\n<p class=\"\" data-start=\"1263\" data-end=\"1283\"><strong data-start=\"1263\" data-end=\"1283\">\u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u0905\u0902\u0924\u0930:<\/strong><\/p>\n<ul data-start=\"1285\" data-end=\"1372\">\n<li class=\"\" data-start=\"1285\" data-end=\"1372\">\n<p class=\"\" data-start=\"1287\" data-end=\"1372\"><span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem]\">\u090f\u0915 \u0938\u092e\u0941\u091a\u094d\u091a\u092f \u092e\u0947\u0902 \u090f\u0915 \u0938\u0947 \u0905\u0927\u093f\u0915 \u092e\u0948\u0915\u094d\u0938\u093f\u092e\u0932 \u092f\u093e \u092e\u093f\u0928\u093f\u092e\u0932 \u0924\u0924\u094d\u0935 \u0939\u094b \u0938\u0915\u0924\u0947 \u0939\u0948\u0902, \u0932\u0947\u0915\u093f\u0928 \u092e\u0948\u0915\u094d\u0938\u093f\u092e\u092e \u0914\u0930 \u092e\u093f\u0928\u093f\u092e\u092e \u0924\u0924\u094d\u0935 \u0905\u0926\u094d\u0935\u093f\u0924\u0940\u092f \u0939\u094b\u0924\u0947 \u0939\u0948\u0902\u0964<\/span>\u200b<\/p>\n<\/li>\n<\/ul>\n<p class=\"\" data-start=\"1374\" data-end=\"1385\"><strong data-start=\"1374\" data-end=\"1385\">\u0909\u0926\u093e\u0939\u0930\u0923:<\/strong><\/p>\n<p class=\"\" data-start=\"1387\" data-end=\"1472\"><span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem]\">\u092e\u093e\u0928 \u0932\u0940\u091c\u093f\u090f, \u0939\u092e\u093e\u0930\u0947 \u092a\u093e\u0938 \u0938\u092e\u0941\u091a\u094d\u091a\u092f <span class=\"katex\"><span class=\"katex-mathml\">P={a,b,c,d}P = \\{a, b, c, d\\}<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">P<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mopen\">{<\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mpunct\">,<\/span><span class=\"mord mathnormal\">b<\/span><span class=\"mpunct\">,<\/span><span class=\"mord mathnormal\">c<\/span><span class=\"mpunct\">,<\/span><span class=\"mord mathnormal\">d<\/span><span class=\"mclose\">}<\/span><\/span><\/span><\/span> \u0939\u0948, \u091c\u0939\u093e\u0901 <span class=\"katex\"><span class=\"katex-mathml\">a\u2264ba \\leq b<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">a<\/span><span class=\"mrel\">\u2264<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">b<\/span><\/span><\/span><\/span>, <span class=\"katex\"><span class=\"katex-mathml\">a\u2264ca \\leq c<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">a<\/span><span class=\"mrel\">\u2264<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">c<\/span><\/span><\/span><\/span>, \u0914\u0930 <span class=\"katex\"><span class=\"katex-mathml\">b\u2264db \\leq d<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">b<\/span><span class=\"mrel\">\u2264<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">d<\/span><\/span><\/span><\/span>\u0964 \u092f\u0939\u093e\u0901:<\/span>\u200b<\/p>\n<ul data-start=\"1474\" data-end=\"1828\">\n<li class=\"\" data-start=\"1474\" data-end=\"1561\">\n<p class=\"\" data-start=\"1476\" data-end=\"1561\"><span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem]\"><strong data-start=\"0\" data-end=\"18\" data-is-only-node=\"\">\u092e\u0948\u0915\u094d\u0938\u093f\u092e\u0932 \u0924\u0924\u094d\u0935:<\/strong> <span class=\"katex\"><span class=\"katex-mathml\">cc<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">c<\/span><\/span><\/span><\/span> \u0914\u0930 <span class=\"katex\"><span class=\"katex-mathml\">dd<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">d<\/span><\/span><\/span><\/span> \u0939\u0948\u0902, \u0915\u094d\u092f\u094b\u0902\u0915\u093f \u0907\u0928\u0915\u0947 \u092c\u093e\u0926 \u0915\u094b\u0908 \u092c\u0921\u093c\u093e \u0924\u0924\u094d\u0935 \u0928\u0939\u0940\u0902 \u0939\u0948\u0964<\/span>\u200b<\/p>\n<\/li>\n<li class=\"\" data-start=\"1563\" data-end=\"1650\">\n<p class=\"\" data-start=\"1565\" data-end=\"1650\"><span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem]\"><strong data-start=\"0\" data-end=\"16\" data-is-only-node=\"\">\u092e\u093f\u0928\u093f\u092e\u0932 \u0924\u0924\u094d\u0935:<\/strong> <span class=\"katex\"><span class=\"katex-mathml\">aa<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">a<\/span><\/span><\/span><\/span> \u0939\u0948, \u0915\u094d\u092f\u094b\u0902\u0915\u093f \u0907\u0938\u0938\u0947 \u092a\u0939\u0932\u0947 \u0915\u094b\u0908 \u091b\u094b\u091f\u093e \u0924\u0924\u094d\u0935 \u0928\u0939\u0940\u0902 \u0939\u0948\u0964<\/span>\u200b<\/p>\n<\/li>\n<li class=\"\" data-start=\"1652\" data-end=\"1739\">\n<p class=\"\" data-start=\"1654\" data-end=\"1739\"><span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem]\"><strong data-start=\"0\" data-end=\"18\" data-is-only-node=\"\">\u092e\u0948\u0915\u094d\u0938\u093f\u092e\u092e \u0924\u0924\u094d\u0935:<\/strong> <span class=\"katex\"><span class=\"katex-mathml\">dd<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">d<\/span><\/span><\/span><\/span> \u0939\u0948, \u0915\u094d\u092f\u094b\u0902\u0915\u093f \u092f\u0939 \u0938\u092d\u0940 \u0924\u0924\u094d\u0935\u094b\u0902 \u0938\u0947 \u092c\u0921\u093c\u093e \u0939\u0948\u0964<\/span>\u200b<\/p>\n<\/li>\n<li class=\"\" data-start=\"1741\" data-end=\"1828\">\n<p class=\"\" data-start=\"1743\" data-end=\"1828\"><span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem]\"><strong data-start=\"0\" data-end=\"16\" data-is-only-node=\"\">\u092e\u093f\u0928\u093f\u092e\u092e \u0924\u0924\u094d\u0935:<\/strong> <span class=\"katex\"><span class=\"katex-mathml\">aa<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">a<\/span><\/span><\/span><\/span> \u0939\u0948, \u0915\u094d\u092f\u094b\u0902\u0915\u093f \u092f\u0939 \u0938\u092d\u0940 \u0924\u0924\u094d\u0935\u094b\u0902 \u0938\u0947 \u091b\u094b\u091f\u093e \u0939\u0948\u0964<\/span>\u200b<\/p>\n<\/li>\n<\/ul>\n<p class=\"\" data-start=\"1830\" data-end=\"1915\"><span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem]\">\u0907\u0928 \u0905\u0935\u0927\u093e\u0930\u0923\u093e\u0913\u0902 \u0915\u094b \u0938\u092e\u091d\u0928\u093e \u0906\u0902\u0936\u093f\u0915 \u0915\u094d\u0930\u092e\u093f\u0924 \u0938\u092e\u0941\u091a\u094d\u091a\u092f\u094b\u0902 \u0914\u0930 \u091c\u093e\u0932\u0915\u094b\u0902 (lattices) \u0915\u0947 \u0905\u0927\u094d\u092f\u092f\u0928 \u092e\u0947\u0902 \u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u0939\u0948\u0964<\/span><\/p>\n<p class=\"\" data-start=\"1830\" data-end=\"1915\">\u200b<\/p>\n<p data-start=\"0\" data-end=\"56\">Here\u2019s a clear explanation in <strong data-start=\"30\" data-end=\"39\">Hindi<\/strong> and English for:<\/p>\n<hr data-start=\"58\" data-end=\"61\" \/>\n<h2 data-start=\"63\" data-end=\"176\">\ud83d\udcd8 <strong data-start=\"69\" data-end=\"176\">Day 03 Part 06 \u2013 Discrete Mathematics (in Hindi): Concept of Maximal and Minimal vs Maximum and Minimum<\/strong><\/h2>\n<hr data-start=\"178\" data-end=\"181\" \/>\n<h3 data-start=\"183\" data-end=\"251\">\ud83d\udd39 <strong data-start=\"190\" data-end=\"251\">1. Maximal \u0914\u0930 Minimal (\u092e\u0948\u0915\u094d\u0938\u093f\u092e\u0932 \u0914\u0930 \u092e\u093f\u0928\u093f\u092e\u0932) \u0915\u094d\u092f\u093e \u0939\u094b\u0924\u0947 \u0939\u0948\u0902?<\/strong><\/h3>\n<h4 data-start=\"253\" data-end=\"300\">\ud83d\udd38 <strong data-start=\"261\" data-end=\"300\">Maximal Element (\u092e\u0948\u0915\u094d\u0938\u093f\u092e\u0932 \u090f\u0932\u093f\u092e\u0947\u0902\u091f):<\/strong><\/h4>\n<ul data-start=\"301\" data-end=\"503\">\n<li data-start=\"301\" data-end=\"393\">\n<p data-start=\"303\" data-end=\"393\">\u090f\u0915 \u0910\u0938\u093e \u090f\u0932\u093f\u092e\u0947\u0902\u091f \u091c\u093f\u0938 \u092a\u0930 \u0915\u094b\u0908 \u0914\u0930 \u090f\u0932\u093f\u092e\u0947\u0902\u091f &#8220;greater&#8221; \u0928\u0939\u0940\u0902 \u0939\u0948 (but not necessarily the greatest).<\/p>\n<\/li>\n<li data-start=\"394\" data-end=\"503\">\n<p data-start=\"396\" data-end=\"503\">\u0907\u0938\u0915\u093e \u092e\u0924\u0932\u092c: \u0909\u0938 \u090f\u0932\u093f\u092e\u0947\u0902\u091f \u0915\u0947 \u092c\u093e\u0926 \u0915\u094b\u0908 \u0926\u0942\u0938\u0930\u093e \u090f\u0932\u093f\u092e\u0947\u0902\u091f \u0928\u0939\u0940\u0902 \u0939\u0948 \u091c\u094b \u0909\u0938\u0938\u0947 \u092c\u0921\u093c\u093e \u0939\u094b <strong data-start=\"467\" data-end=\"502\">\u0914\u0930 \u0909\u0938\u0938\u0947 \u0938\u0902\u092c\u0902\u0927\u093f\u0924 \u092d\u0940 \u0939\u094b (related)<\/strong>\u0964<\/p>\n<\/li>\n<\/ul>\n<p data-start=\"505\" data-end=\"567\">\ud83e\uddfe <strong data-start=\"508\" data-end=\"518\">\u0909\u0926\u093e\u0939\u0930\u0923<\/strong>:<br \/>\nSet: {a, b, c, d} with relation: a &lt; b, a &lt; c<\/p>\n<ul data-start=\"568\" data-end=\"646\">\n<li data-start=\"568\" data-end=\"646\">\n<p data-start=\"570\" data-end=\"646\">\u092f\u0939\u093e\u0901 b \u0914\u0930 c \u0926\u094b\u0928\u094b\u0902 <strong data-start=\"588\" data-end=\"600\">\u092e\u0948\u0915\u094d\u0938\u093f\u092e\u0932<\/strong> \u0939\u094b \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0905\u0917\u0930 \u0909\u0928\u0915\u0947 \u090a\u092a\u0930 \u0915\u094b\u0908 \u090f\u0932\u093f\u092e\u0947\u0902\u091f \u0928\u0939\u0940\u0902 \u0939\u0948\u0964<\/p>\n<\/li>\n<\/ul>\n<hr data-start=\"648\" data-end=\"651\" \/>\n<h4 data-start=\"653\" data-end=\"698\">\ud83d\udd38 <strong data-start=\"661\" data-end=\"698\">Minimal Element (\u092e\u093f\u0928\u093f\u092e\u0932 \u090f\u0932\u093f\u092e\u0947\u0902\u091f):<\/strong><\/h4>\n<ul data-start=\"699\" data-end=\"846\">\n<li data-start=\"699\" data-end=\"785\">\n<p data-start=\"701\" data-end=\"785\">\u090f\u0915 \u0910\u0938\u093e \u090f\u0932\u093f\u092e\u0947\u0902\u091f \u091c\u093f\u0938\u0915\u0947 \u0928\u0940\u091a\u0947 \u0915\u094b\u0908 \u0914\u0930 \u090f\u0932\u093f\u092e\u0947\u0902\u091f \u0928\u0939\u0940\u0902 \u0939\u0948 (but not necessarily the smallest).<\/p>\n<\/li>\n<li data-start=\"786\" data-end=\"846\">\n<p data-start=\"788\" data-end=\"846\">\u092e\u0924\u0932\u092c: \u0909\u0938\u0938\u0947 \u091b\u094b\u091f\u093e \u0915\u094b\u0908 \u0914\u0930 \u090f\u0932\u093f\u092e\u0947\u0902\u091f \u0928\u0939\u0940\u0902 \u0939\u0948 \u091c\u094b \u0909\u0938\u0938\u0947 \u0938\u0902\u092c\u0902\u0927\u093f\u0924 \u0939\u094b\u0964<\/p>\n<\/li>\n<\/ul>\n<p data-start=\"848\" data-end=\"862\">\ud83e\uddfe <strong data-start=\"851\" data-end=\"861\">\u0909\u0926\u093e\u0939\u0930\u0923<\/strong>:<\/p>\n<ul data-start=\"863\" data-end=\"918\">\n<li data-start=\"863\" data-end=\"918\">\n<p data-start=\"865\" data-end=\"918\">\u090a\u092a\u0930 \u0915\u0947 \u0909\u0926\u093e\u0939\u0930\u0923 \u092e\u0947\u0902 a \u090f\u0915 <strong data-start=\"888\" data-end=\"898\">\u092e\u093f\u0928\u093f\u092e\u0932<\/strong> \u090f\u0932\u093f\u092e\u0947\u0902\u091f \u0939\u094b \u0938\u0915\u0924\u093e \u0939\u0948\u0964<\/p>\n<\/li>\n<\/ul>\n<hr data-start=\"920\" data-end=\"923\" \/>\n<h3 data-start=\"925\" data-end=\"972\">\ud83d\udd39 <strong data-start=\"932\" data-end=\"972\">2. Maximum \u0914\u0930 Minimum \u0915\u094d\u092f\u093e \u0939\u094b\u0924\u0947 \u0939\u0948\u0902?<\/strong><\/h3>\n<h4 data-start=\"974\" data-end=\"1003\">\ud83d\udd38 <strong data-start=\"982\" data-end=\"1003\">Maximum (\u0905\u0927\u093f\u0915\u0924\u092e):<\/strong><\/h4>\n<ul data-start=\"1004\" data-end=\"1077\">\n<li data-start=\"1004\" data-end=\"1077\">\n<p data-start=\"1006\" data-end=\"1077\">\u0910\u0938\u093e \u090f\u0932\u093f\u092e\u0947\u0902\u091f \u091c\u094b \u0938\u0947\u091f \u092e\u0947\u0902 \u0938\u092c\u0938\u0947 \u092c\u0921\u093c\u093e \u0939\u094b \u0914\u0930 <strong data-start=\"1045\" data-end=\"1073\">\u0938\u092d\u0940 \u090f\u0932\u093f\u092e\u0947\u0902\u091f\u094d\u0938 \u0938\u0947 related<\/strong> \u0939\u094b\u0964<\/p>\n<\/li>\n<\/ul>\n<h4 data-start=\"1079\" data-end=\"1109\">\ud83d\udd38 <strong data-start=\"1087\" data-end=\"1109\">Minimum (\u0928\u094d\u092f\u0942\u0928\u0924\u092e):<\/strong><\/h4>\n<ul data-start=\"1110\" data-end=\"1183\">\n<li data-start=\"1110\" data-end=\"1183\">\n<p data-start=\"1112\" data-end=\"1183\">\u0910\u0938\u093e \u090f\u0932\u093f\u092e\u0947\u0902\u091f \u091c\u094b \u0938\u0947\u091f \u092e\u0947\u0902 \u0938\u092c\u0938\u0947 \u091b\u094b\u091f\u093e \u0939\u094b \u0914\u0930 <strong data-start=\"1151\" data-end=\"1179\">\u0938\u092d\u0940 \u090f\u0932\u093f\u092e\u0947\u0902\u091f\u094d\u0938 \u0938\u0947 related<\/strong> \u0939\u094b\u0964<\/p>\n<\/li>\n<\/ul>\n<hr data-start=\"1185\" data-end=\"1188\" \/>\n<h3 data-start=\"1190\" data-end=\"1230\">\ud83d\udccc <strong data-start=\"1197\" data-end=\"1230\">Main Difference (\u092e\u0941\u0916\u094d\u092f \u0905\u0902\u0924\u0930):<\/strong><\/h3>\n<div class=\"_tableContainer_16hzy_1\">\n<div class=\"_tableWrapper_16hzy_14 group flex w-fit flex-col-reverse\">\n<table class=\"w-fit min-w-(--thread-content-width)\" data-start=\"1232\" data-end=\"1824\">\n<thead data-start=\"1232\" data-end=\"1326\">\n<tr data-start=\"1232\" data-end=\"1326\">\n<th data-start=\"1232\" data-end=\"1253\" data-col-size=\"sm\">Concept<\/th>\n<th data-start=\"1253\" data-end=\"1307\" data-col-size=\"sm\">\u092e\u0924\u0932\u092c (Meaning)<\/th>\n<th data-start=\"1307\" data-end=\"1326\" data-col-size=\"sm\">Unique \u0939\u094b\u0924\u093e \u0939\u0948?<\/th>\n<\/tr>\n<\/thead>\n<tbody data-start=\"1423\" data-end=\"1824\">\n<tr data-start=\"1423\" data-end=\"1526\">\n<td data-start=\"1423\" data-end=\"1444\" data-col-size=\"sm\"><strong data-start=\"1425\" data-end=\"1436\">Maximal<\/strong><\/td>\n<td data-col-size=\"sm\" data-start=\"1444\" data-end=\"1498\">\u0915\u094b\u0908 \u0914\u0930 related \u092c\u0921\u093c\u093e \u090f\u0932\u093f\u092e\u0947\u0902\u091f \u0928\u0939\u0940\u0902 \u0939\u0948<\/td>\n<td data-col-size=\"sm\" data-start=\"1498\" data-end=\"1526\">\u274c (Multiple \u0939\u094b \u0938\u0915\u0924\u0947 \u0939\u0948\u0902)<\/td>\n<\/tr>\n<tr data-start=\"1527\" data-end=\"1623\">\n<td data-start=\"1527\" data-end=\"1548\" data-col-size=\"sm\"><strong data-start=\"1529\" data-end=\"1540\">Maximum<\/strong><\/td>\n<td data-col-size=\"sm\" data-start=\"1548\" data-end=\"1602\">\u0938\u092d\u0940 \u090f\u0932\u093f\u092e\u0947\u0902\u091f\u094d\u0938 \u0938\u0947 \u092c\u0921\u093c\u093e \u0914\u0930 related<\/td>\n<td data-col-size=\"sm\" data-start=\"1602\" data-end=\"1623\">\u2705 (\u090f\u0915 \u0939\u0940 \u0939\u094b\u0924\u093e \u0939\u0948)<\/td>\n<\/tr>\n<tr data-start=\"1624\" data-end=\"1727\">\n<td data-start=\"1624\" data-end=\"1645\" data-col-size=\"sm\"><strong data-start=\"1626\" data-end=\"1637\">Minimal<\/strong><\/td>\n<td data-col-size=\"sm\" data-start=\"1645\" data-end=\"1699\">\u0915\u094b\u0908 \u0914\u0930 related \u091b\u094b\u091f\u093e \u090f\u0932\u093f\u092e\u0947\u0902\u091f \u0928\u0939\u0940\u0902 \u0939\u0948<\/td>\n<td data-col-size=\"sm\" data-start=\"1699\" data-end=\"1727\">\u274c (Multiple \u0939\u094b \u0938\u0915\u0924\u0947 \u0939\u0948\u0902)<\/td>\n<\/tr>\n<tr data-start=\"1728\" data-end=\"1824\">\n<td data-start=\"1728\" data-end=\"1749\" data-col-size=\"sm\"><strong data-start=\"1730\" data-end=\"1741\">Minimum<\/strong><\/td>\n<td data-col-size=\"sm\" data-start=\"1749\" data-end=\"1803\">\u0938\u092d\u0940 \u090f\u0932\u093f\u092e\u0947\u0902\u091f\u094d\u0938 \u0938\u0947 \u091b\u094b\u091f\u093e \u0914\u0930 related<\/td>\n<td data-col-size=\"sm\" data-start=\"1803\" data-end=\"1824\">\u2705 (\u090f\u0915 \u0939\u0940 \u0939\u094b\u0924\u093e \u0939\u0948)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class=\"sticky end-(--thread-content-margin) h-0 self-end select-none\">\n<div class=\"absolute end-0 flex items-end\"><\/div>\n<\/div>\n<\/div>\n<\/div>\n<hr data-start=\"1826\" data-end=\"1829\" \/>\n<h3 data-start=\"1831\" data-end=\"1860\">\ud83e\udde0 <strong data-start=\"1838\" data-end=\"1860\">Example for All 4:<\/strong><\/h3>\n<p data-start=\"1861\" data-end=\"1903\">Let\u2019s say we have a partially ordered set:<\/p>\n<div class=\"contain-inline-size rounded-md border-[0.5px] border-token-border-medium relative bg-token-sidebar-surface-primary\">\n<div class=\"flex items-center text-token-text-secondary px-4 py-2 text-xs font-sans justify-between h-9 bg-token-sidebar-surface-primary dark:bg-token-main-surface-secondary select-none rounded-t-[5px]\">ini<\/div>\n<div class=\"sticky top-9\">\n<div class=\"absolute end-0 bottom-0 flex h-9 items-center pe-2\">\n<div class=\"bg-token-sidebar-surface-primary text-token-text-secondary dark:bg-token-main-surface-secondary flex items-center rounded-sm px-2 font-sans text-xs\"><button class=\"flex gap-1 items-center select-none px-4 py-1\" aria-label=\"Copy\">Copy<\/button><span class=\"\" data-state=\"closed\"><button class=\"flex items-center gap-1 px-4 py-1 select-none\">Edit<\/button><\/span><\/div>\n<\/div>\n<\/div>\n<div class=\"overflow-y-auto p-4\" dir=\"ltr\"><code class=\"whitespace-pre!\"><span class=\"hljs-attr\">A<\/span> = {<span class=\"hljs-number\">1<\/span>, <span class=\"hljs-number\">2<\/span>, <span class=\"hljs-number\">3<\/span>}, with relation \u2264<br \/>\n<\/code><\/div>\n<\/div>\n<ul data-start=\"1944\" data-end=\"2033\">\n<li data-start=\"1944\" data-end=\"1966\">\n<p data-start=\"1946\" data-end=\"1966\"><strong data-start=\"1946\" data-end=\"1957\">Maximum<\/strong> = 3 \u2714\ufe0f<\/p>\n<\/li>\n<li data-start=\"1967\" data-end=\"1989\">\n<p data-start=\"1969\" data-end=\"1989\"><strong data-start=\"1969\" data-end=\"1980\">Maximal<\/strong> = 3 \u2714\ufe0f<\/p>\n<\/li>\n<li data-start=\"1990\" data-end=\"2012\">\n<p data-start=\"1992\" data-end=\"2012\"><strong data-start=\"1992\" data-end=\"2003\">Minimum<\/strong> = 1 \u2714\ufe0f<\/p>\n<\/li>\n<li data-start=\"2013\" data-end=\"2033\">\n<p data-start=\"2015\" data-end=\"2033\"><strong data-start=\"2015\" data-end=\"2026\">Minimal<\/strong> = 1 \u2714\ufe0f<\/p>\n<\/li>\n<\/ul>\n<p data-start=\"2035\" data-end=\"2069\">But in complex sets, you can have:<\/p>\n<ul data-start=\"2070\" data-end=\"2151\">\n<li data-start=\"2070\" data-end=\"2100\">\n<p data-start=\"2072\" data-end=\"2100\">Multiple <strong data-start=\"2081\" data-end=\"2100\">maximal\/minimal<\/strong><\/p>\n<\/li>\n<li data-start=\"2101\" data-end=\"2151\">\n<p data-start=\"2103\" data-end=\"2151\">But <strong data-start=\"2107\" data-end=\"2119\">only one<\/strong> maximum\/minimum (if they exist)<\/p>\n<\/li>\n<\/ul>\n<hr data-start=\"2153\" data-end=\"2156\" \/>\n<h3 data-start=\"2158\" data-end=\"2187\">\ud83d\udcda Conclusion (\u0928\u093f\u0937\u094d\u0915\u0930\u094d\u0937):<\/h3>\n<ul data-start=\"2189\" data-end=\"2403\">\n<li data-start=\"2189\" data-end=\"2257\">\n<p data-start=\"2191\" data-end=\"2257\"><strong data-start=\"2191\" data-end=\"2210\">Maximal\/Minimal<\/strong> \u2192 \u092c\u0938 \u0906\u0917\u0947 \u092f\u093e \u092a\u0940\u091b\u0947 \u0915\u094b\u0908 element \u0928\u0939\u0940\u0902 \u0939\u094b\u0928\u093e \u091a\u093e\u0939\u093f\u090f<\/p>\n<\/li>\n<li data-start=\"2258\" data-end=\"2339\">\n<p data-start=\"2260\" data-end=\"2339\"><strong data-start=\"2260\" data-end=\"2279\">Maximum\/Minimum<\/strong> \u2192 \u092a\u0942\u0930\u0947 \u0938\u0947\u091f \u0915\u0947 comparison \u092e\u0947\u0902 \u0938\u092c\u0938\u0947 \u092c\u0921\u093c\u093e \u092f\u093e \u091b\u094b\u091f\u093e \u0939\u094b\u0928\u093e \u091a\u093e\u0939\u093f\u090f<\/p>\n<\/li>\n<li data-start=\"2340\" data-end=\"2403\">\n<p data-start=\"2342\" data-end=\"2403\"><strong data-start=\"2342\" data-end=\"2359\">Partial order<\/strong> \u092e\u0947\u0902 maximal\/minimal \u091c\u093c\u094d\u092f\u093e\u0926\u093e common \u0939\u094b\u0924\u0947 \u0939\u0948\u0902<\/p>\n<\/li>\n<\/ul>\n<hr data-start=\"2405\" data-end=\"2408\" \/>\n<p data-start=\"2410\" data-end=\"2474\" data-is-last-node=\"\" data-is-only-node=\"\">Would you like a <strong data-start=\"2427\" data-end=\"2455\">diagram or Hasse diagram<\/strong> to visualize this?<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Day 03Part 06-Discrete Mathematics in Hindi-Concept of maximal and minimal with maximum and minimum. [fvplayer id=&#8221;225&#8243;] \u200b\u0921\u093f\u0938\u094d\u0915\u094d\u0930\u0940\u091f \u0917\u0923\u093f\u0924 \u092e\u0947\u0902, \u092e\u0948\u0915\u094d\u0938\u093f\u092e\u0932 (\u0938\u0930\u094d\u0935\u094b\u091a\u094d\u091a) \u0914\u0930 \u092e\u093f\u0928\u093f\u092e\u0932 (\u0928\u094d\u092f\u0942\u0928\u0924\u092e) \u0924\u0924\u094d\u0935\u094b\u0902 \u0915\u0940 \u0905\u0935\u0927\u093e\u0930\u0923\u093e \u0906\u0902\u0936\u093f\u0915 \u0915\u094d\u0930\u092e\u093f\u0924 \u0938\u092e\u0941\u091a\u094d\u091a\u092f\u094b\u0902 (partially ordered sets) \u092e\u0947\u0902 \u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u092d\u0942\u092e\u093f\u0915\u093e \u0928\u093f\u092d\u093e\u0924\u0940 \u0939\u0948\u0964 \u0907\u0928 \u0905\u0935\u0927\u093e\u0930\u0923\u093e\u0913\u0902 \u0915\u094b \u0938\u092e\u091d\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f, \u0939\u092e\u0947\u0902 \u092a\u0939\u0932\u0947 \u0906\u0902\u0936\u093f\u0915 \u0915\u094d\u0930\u092e \u0914\u0930 \u0906\u0902\u0936\u093f\u0915 \u0915\u094d\u0930\u092e\u093f\u0924 \u0938\u092e\u0941\u091a\u094d\u091a\u092f \u0915\u0940 \u0938\u092e\u091d \u0939\u094b\u0928\u0940 [&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-3033","post","type-post","status-publish","format-standard","hentry","category-discrete-mathematics"],"_links":{"self":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts\/3033","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=3033"}],"version-history":[{"count":0,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts\/3033\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/media?parent=3033"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/categories?post=3033"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/tags?post=3033"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}