{"id":3150,"date":"2025-06-02T07:27:16","date_gmt":"2025-06-02T07:27:16","guid":{"rendered":"https:\/\/diznr.com\/?p=3150"},"modified":"2025-06-02T07:27:16","modified_gmt":"2025-06-02T07:27:16","slug":"day-01-discrete-mathematics-for-gate-in-hindi-cseit-concept-of-universal-set-and-complement-of-set","status":"publish","type":"post","link":"https:\/\/www.reilsolar.com\/pdf\/day-01-discrete-mathematics-for-gate-in-hindi-cseit-concept-of-universal-set-and-complement-of-set\/","title":{"rendered":"Day 01- Discrete Mathematics for gate in Hindi CSEIT- Concept of Universal set and Complement of set"},"content":{"rendered":"<p>Day 01- Discrete Mathematics for gate in Hindi CSEIT- Concept of Universal set and Complement of set<\/p>\n<p>[fvplayer id=&#8221;275&#8243;]<\/p>\n<h3 data-start=\"0\" data-end=\"99\"><strong data-start=\"3\" data-end=\"97\">Day 01: \u0921\u093f\u0938\u094d\u0915\u094d\u0930\u0940\u091f \u092e\u0948\u0925\u092e\u0947\u091f\u093f\u0915\u094d\u0938 (Discrete Mathematics) &#8211; \u092f\u0942\u0928\u093f\u0935\u0930\u094d\u0938\u0932 \u0938\u0947\u091f \u0914\u0930 \u0915\u092e\u094d\u092a\u094d\u0932\u0940\u092e\u0947\u0902\u091f \u0911\u092b\u093c \u0938\u0947\u091f<\/strong><\/h3>\n<h3 data-start=\"101\" data-end=\"222\"><strong data-start=\"101\" data-end=\"220\">\u092f\u0939 \u091f\u0949\u092a\u093f\u0915 GATE (CSE\/IT) \u0915\u0947 \u0932\u093f\u090f \u092c\u0939\u0941\u0924 \u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u0939\u0948, \u0915\u094d\u092f\u094b\u0902\u0915\u093f \u0938\u0947\u091f \u0925\u094d\u092f\u094b\u0930\u0940 (Set Theory) \u0938\u0947 \u0905\u0915\u094d\u0938\u0930 \u092a\u094d\u0930\u0936\u094d\u0928 \u092a\u0942\u091b\u0947 \u091c\u093e\u0924\u0947 \u0939\u0948\u0902\u0964<\/strong><\/h3>\n<h3 data-start=\"229\" data-end=\"284\"><strong data-start=\"232\" data-end=\"282\">\u00a0\u092f\u0942\u0928\u093f\u0935\u0930\u094d\u0938\u0932 \u0938\u0947\u091f (Universal Set) \u0915\u094d\u092f\u093e \u0939\u094b\u0924\u093e \u0939\u0948?<\/strong><\/h3>\n<p data-start=\"285\" data-end=\"409\">\u092f\u0942\u0928\u093f\u0935\u0930\u094d\u0938\u0932 \u0938\u0947\u091f \u0935\u0939 \u0938\u0947\u091f \u0939\u094b\u0924\u093e \u0939\u0948 \u091c\u093f\u0938\u092e\u0947\u0902 <strong data-start=\"321\" data-end=\"352\">\u0938\u092d\u0940 \u0938\u0902\u092c\u0902\u0927\u093f\u0924 \u0924\u0924\u094d\u0935 (elements)<\/strong> \u092e\u094c\u091c\u0942\u0926 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902\u0964 \u0907\u0938\u0947 \u0906\u092e\u0924\u094c\u0930 \u092a\u0930 <strong data-start=\"382\" data-end=\"387\">U<\/strong> \u0938\u0947 \u0926\u0930\u094d\u0936\u093e\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964<\/p>\n<h3 data-start=\"411\" data-end=\"430\"><strong data-start=\"415\" data-end=\"428\">\u00a0\u0909\u0926\u093e\u0939\u0930\u0923<\/strong><\/h3>\n<p data-start=\"431\" data-end=\"466\">\u092f\u0926\u093f \u0939\u092e\u093e\u0930\u0947 \u092a\u093e\u0938 \u0924\u0940\u0928 \u0938\u0947\u091f \u0926\u093f\u090f \u0917\u090f \u0939\u0948\u0902:<\/p>\n<ul data-start=\"467\" data-end=\"532\">\n<li data-start=\"467\" data-end=\"488\"><strong data-start=\"469\" data-end=\"486\">A = {1, 2, 3}<\/strong><\/li>\n<li data-start=\"489\" data-end=\"510\"><strong data-start=\"491\" data-end=\"508\">B = {3, 4, 5}<\/strong><\/li>\n<li data-start=\"511\" data-end=\"532\"><strong data-start=\"513\" data-end=\"530\">C = {5, 6, 7}<\/strong><\/li>\n<\/ul>\n<p data-start=\"534\" data-end=\"638\">\u0914\u0930 \u0905\u0917\u0930 \u092f\u0947 \u0938\u092d\u0940 <strong data-start=\"548\" data-end=\"583\">U = {1, 2, 3, 4, 5, 6, 7, 8, 9}<\/strong> \u092e\u0947\u0902 \u092e\u094c\u091c\u0942\u0926 \u0939\u0948\u0902, \u0924\u094b <strong data-start=\"602\" data-end=\"627\">U \u0939\u092e\u093e\u0930\u093e \u092f\u0942\u0928\u093f\u0935\u0930\u094d\u0938\u0932 \u0938\u0947\u091f<\/strong> \u0915\u0939\u0932\u093e\u090f\u0917\u093e\u0964<\/p>\n<p data-start=\"640\" data-end=\"665\"><strong data-start=\"642\" data-end=\"663\">\u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u092c\u093e\u0924\u0947\u0902:<\/strong><\/p>\n<ul data-start=\"666\" data-end=\"859\">\n<li data-start=\"666\" data-end=\"728\"><strong data-start=\"668\" data-end=\"726\">\u092f\u0942\u0928\u093f\u0935\u0930\u094d\u0938\u0932 \u0938\u0947\u091f \u0915\u0940 \u092a\u0930\u093f\u092d\u093e\u0937\u093e \u092a\u094d\u0930\u0936\u094d\u0928 \u0915\u0947 \u0905\u0928\u0941\u0938\u093e\u0930 \u092c\u0926\u0932 \u0938\u0915\u0924\u0940 \u0939\u0948\u0964<\/strong><\/li>\n<li data-start=\"729\" data-end=\"782\"><strong data-start=\"731\" data-end=\"780\">\u0938\u092d\u0940 \u0938\u0947\u091f \u0909\u0938\u0940 \u092f\u0942\u0928\u093f\u0935\u0930\u094d\u0938\u0932 \u0938\u0947\u091f \u0915\u093e \u0939\u093f\u0938\u094d\u0938\u093e \u0939\u094b\u0924\u0947 \u0939\u0948\u0902\u0964<\/strong><\/li>\n<li data-start=\"783\" data-end=\"859\"><strong data-start=\"785\" data-end=\"857\">U \u0915\u093e \u0915\u092e\u094d\u092a\u094d\u0932\u0940\u092e\u0947\u0902\u091f (U&#8217;) \u0928\u0939\u0940\u0902 \u0939\u094b\u0924\u093e, \u0915\u094d\u092f\u094b\u0902\u0915\u093f U \u0915\u0947 \u092c\u093e\u0939\u0930 \u0915\u0941\u091b \u092d\u0940 \u0928\u0939\u0940\u0902 \u0939\u094b\u0924\u093e\u0964<\/strong><\/li>\n<\/ul>\n<h3 data-start=\"866\" data-end=\"933\"><strong data-start=\"869\" data-end=\"931\">\u00a0\u0915\u092e\u094d\u092a\u094d\u0932\u0940\u092e\u0947\u0902\u091f \u0911\u092b\u093c \u0938\u0947\u091f (Complement of a Set) \u0915\u094d\u092f\u093e \u0939\u094b\u0924\u093e \u0939\u0948?<\/strong><\/h3>\n<p data-start=\"934\" data-end=\"1080\">\u0905\u0917\u0930 \u0915\u094b\u0908 \u0938\u0947\u091f <strong data-start=\"946\" data-end=\"951\">A<\/strong> \u092f\u0942\u0928\u093f\u0935\u0930\u094d\u0938\u0932 \u0938\u0947\u091f <strong data-start=\"966\" data-end=\"971\">U<\/strong> \u0915\u093e \u090f\u0915 \u0939\u093f\u0938\u094d\u0938\u093e \u0939\u0948, \u0924\u094b \u0909\u0938\u0915\u093e <strong data-start=\"997\" data-end=\"1016\">Complement (A&#8217;)<\/strong> \u0909\u0928 \u0924\u0924\u094d\u0935\u094b\u0902 \u0915\u093e \u0938\u0947\u091f \u0939\u094b\u0917\u093e \u091c\u094b <strong data-start=\"1042\" data-end=\"1078\">U \u092e\u0947\u0902 \u0939\u0948\u0902, \u0932\u0947\u0915\u093f\u0928 A \u092e\u0947\u0902 \u0928\u0939\u0940\u0902 \u0939\u0948\u0902\u0964<\/strong><\/p>\n<h3 data-start=\"1082\" data-end=\"1109\"><strong data-start=\"1086\" data-end=\"1107\">\u00a0\u0917\u0923\u093f\u0924\u0940\u092f \u092a\u0930\u093f\u092d\u093e\u0937\u093e<\/strong><\/h3>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">A\u2032=U\u2212AA&#8217; = U &#8211; A<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">U<\/span><span class=\"mbin\">\u2212<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">A<\/span><\/span><\/span><\/span><\/span><\/p>\n<p data-start=\"1129\" data-end=\"1136\">\u091c\u0939\u093e\u0901,<\/p>\n<ul data-start=\"1137\" data-end=\"1214\">\n<li data-start=\"1137\" data-end=\"1214\"><strong data-start=\"1139\" data-end=\"1163\">A&#8217; (Complement of A)<\/strong> = \u0935\u0947 \u0924\u0924\u094d\u0935 \u091c\u094b <strong data-start=\"1177\" data-end=\"1212\">U \u092e\u0947\u0902 \u0939\u0948\u0902 \u0932\u0947\u0915\u093f\u0928 A \u092e\u0947\u0902 \u0928\u0939\u0940\u0902 \u0939\u0948\u0902\u0964<\/strong><\/li>\n<\/ul>\n<h3 data-start=\"1216\" data-end=\"1235\"><strong data-start=\"1220\" data-end=\"1233\">\u00a0\u0909\u0926\u093e\u0939\u0930\u0923<\/strong><\/h3>\n<p data-start=\"1236\" data-end=\"1319\">\u092e\u093e\u0928 \u0932\u0940\u091c\u093f\u090f <strong data-start=\"1246\" data-end=\"1281\">U = {1, 2, 3, 4, 5, 6, 7, 8, 9}<\/strong> \u0914\u0930<br data-start=\"1284\" data-end=\"1287\" \/><strong data-start=\"1287\" data-end=\"1307\">A = {1, 2, 3, 4}<\/strong> \u0939\u0948\u0964<br data-start=\"1311\" data-end=\"1314\" \/>\u0924\u094b,<\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">A\u2032=U\u2212A={5,6,7,8,9}A&#8217; = U &#8211; A = \\{5, 6, 7, 8, 9\\}<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">U<\/span><span class=\"mbin\">\u2212<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">A<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mopen\">{<\/span><span class=\"mord\">5<\/span><span class=\"mpunct\">,<\/span><span class=\"mord\">6<\/span><span class=\"mpunct\">,<\/span><span class=\"mord\">7<\/span><span class=\"mpunct\">,<\/span><span class=\"mord\">8<\/span><span class=\"mpunct\">,<\/span><span class=\"mord\">9<\/span><span class=\"mclose\">}<\/span><\/span><\/span><\/span><\/span><\/p>\n<p data-start=\"1360\" data-end=\"1385\"><strong data-start=\"1362\" data-end=\"1383\">\u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u092c\u093e\u0924\u0947\u0902:<\/strong><\/p>\n<ul data-start=\"1386\" data-end=\"1556\">\n<li data-start=\"1386\" data-end=\"1471\"><strong data-start=\"1388\" data-end=\"1402\">A&#8217; + A = U<\/strong> (\u0938\u0947\u091f A \u0914\u0930 \u0909\u0938\u0915\u0947 \u0915\u092e\u094d\u092a\u094d\u0932\u0940\u092e\u0947\u0902\u091f \u0915\u094b \u092e\u093f\u0932\u093e\u0928\u0947 \u092a\u0930 \u092f\u0942\u0928\u093f\u0935\u0930\u094d\u0938\u0932 \u0938\u0947\u091f \u092c\u0928 \u091c\u093e\u0924\u093e \u0939\u0948)\u0964<\/li>\n<li data-start=\"1472\" data-end=\"1556\"><strong data-start=\"1474\" data-end=\"1488\">A \u2229 A&#8217; = \u2205<\/strong> (\u0938\u0947\u091f A \u0914\u0930 \u0909\u0938\u0915\u0947 \u0915\u092e\u094d\u092a\u094d\u0932\u0940\u092e\u0947\u0902\u091f \u0915\u093e \u0907\u0902\u091f\u0930\u0938\u0947\u0915\u094d\u0936\u0928 \u0939\u092e\u0947\u0936\u093e \u0916\u093e\u0932\u0940 \u0938\u0947\u091f \u0939\u094b\u0924\u093e \u0939\u0948)\u0964<\/li>\n<\/ul>\n<h3 data-start=\"1563\" data-end=\"1600\"><strong data-start=\"1566\" data-end=\"1598\">\u0935\u0947\u0928 \u0921\u093e\u092f\u0917\u094d\u0930\u093e\u092e \u0926\u094d\u0935\u093e\u0930\u093e \u0938\u092e\u091d\u0947\u0902<\/strong><\/h3>\n<p data-start=\"1602\" data-end=\"1785\"><strong data-start=\"1605\" data-end=\"1657\">\u092f\u0942\u0928\u093f\u0935\u0930\u094d\u0938\u0932 \u0938\u0947\u091f (U) \u0915\u094b \u090f\u0915 \u092c\u0921\u093c\u093e \u092c\u0949\u0915\u094d\u0938 \u092e\u093e\u0928 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964<\/strong><br data-start=\"1657\" data-end=\"1660\" \/><strong data-start=\"1663\" data-end=\"1708\">\u0938\u0947\u091f A \u0907\u0938 \u092c\u0949\u0915\u094d\u0938 \u0915\u0947 \u0905\u0902\u0926\u0930 \u090f\u0915 \u091b\u094b\u091f\u093e \u0917\u094b\u0932\u093e \u0939\u094b\u0917\u093e\u0964<\/strong><br data-start=\"1708\" data-end=\"1711\" \/><strong data-start=\"1714\" data-end=\"1783\">A&#8217; (A \u0915\u093e \u0915\u092e\u094d\u092a\u094d\u0932\u0940\u092e\u0947\u0902\u091f) \u092c\u0949\u0915\u094d\u0938 \u0915\u093e \u0935\u0939 \u0939\u093f\u0938\u094d\u0938\u093e \u0939\u094b\u0917\u093e \u091c\u094b \u0917\u094b\u0932\u0947 \u0915\u0947 \u092c\u093e\u0939\u0930 \u0939\u0948\u0964<\/strong><\/p>\n<p data-start=\"1787\" data-end=\"1817\"><strong data-start=\"1787\" data-end=\"1817\">\u00a0\u0909\u0926\u093e\u0939\u0930\u0923 \u0915\u093e \u0935\u0947\u0928 \u0921\u093e\u092f\u0917\u094d\u0930\u093e\u092e:<\/strong><\/p>\n<div class=\"contain-inline-size rounded-md border-[0.5px] border-token-border-medium relative bg-token-sidebar-surface-primary dark:bg-gray-950\">\n<div class=\"flex items-center text-token-text-secondary px-4 py-2 text-xs font-sans justify-between rounded-t-[5px] h-9 bg-token-sidebar-surface-primary dark:bg-token-main-surface-secondary select-none\">markdown<\/div>\n<div class=\"sticky top-9 md:top-[5.75rem]\">\n<div class=\"absolute bottom-0 right-2 flex h-9 items-center\">\n<div class=\"flex items-center rounded bg-token-sidebar-surface-primary px-2 font-sans text-xs text-token-text-secondary dark:bg-token-main-surface-secondary\"><span class=\"\" data-state=\"closed\"><button class=\"flex gap-1 items-center select-none px-4 py-1\" aria-label=\"Copy\">Copy<\/button><\/span><span class=\"\" data-state=\"closed\"><button class=\"flex select-none items-center gap-1\">Edit<\/button><\/span><\/div>\n<\/div>\n<\/div>\n<div class=\"overflow-y-auto p-4\" dir=\"ltr\"><code class=\"!whitespace-pre\">-------------------------<br \/>\n|       U (Universal)  |<br \/>\n|  --------------      |<br \/>\n|  |   A        | A'  |<br \/>\n<span class=\"hljs-section\">|  --------------      |<br \/>\n------------------------<\/span><br \/>\n<\/code><\/div>\n<\/div>\n<h3 data-start=\"1983\" data-end=\"2036\"><strong data-start=\"1986\" data-end=\"2034\">\u0915\u0941\u091b \u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u0938\u0942\u0924\u094d\u0930 (Important Formulas)<\/strong><\/h3>\n<p data-start=\"2038\" data-end=\"2085\">1\ufe0f\u20e3 <strong data-start=\"2042\" data-end=\"2083\">\u0921\u093f \u092e\u0949\u0930\u094d\u0917\u0928 \u0915\u0947 \u0928\u093f\u092f\u092e (De Morgan\u2019s Laws):<\/strong><\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">(A\u222aB)\u2032=A\u2032\u2229B\u2032(A \u222a B)&#8217; = A&#8217; \u2229 B&#8217;<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mbin\">\u222a<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">B<\/span><span class=\"mclose\">)<span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin\">\u2229<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">B<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> <span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">(A\u2229B)\u2032=A\u2032\u222aB\u2032(A \u2229 B)&#8217; = A&#8217; \u222a B&#8217;<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mbin\">\u2229<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">B<\/span><span class=\"mclose\">)<span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin\">\u222a<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">B<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<p data-start=\"2141\" data-end=\"2215\">2\ufe0f\u20e3 <strong data-start=\"2145\" data-end=\"2213\">\u0915\u093f\u0938\u0940 \u092d\u0940 \u0938\u0947\u091f \u0914\u0930 \u0909\u0938\u0915\u0947 \u0915\u092e\u094d\u092a\u094d\u0932\u0940\u092e\u0947\u0902\u091f \u0915\u093e \u092e\u093f\u0932\u093e\u0915\u0930 \u092f\u0942\u0928\u093f\u0935\u0930\u094d\u0938\u0932 \u0938\u0947\u091f \u092c\u0928\u0924\u093e \u0939\u0948:<\/strong><\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">A\u222aA\u2032=UA \u222a A&#8217; = U<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">A<\/span><span class=\"mbin\">\u222a<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">U<\/span><\/span><\/span><\/span><\/span><\/p>\n<p data-start=\"2236\" data-end=\"2315\">3\ufe0f\u20e3 <strong data-start=\"2240\" data-end=\"2313\">\u0915\u093f\u0938\u0940 \u092d\u0940 \u0938\u0947\u091f \u0914\u0930 \u0909\u0938\u0915\u0947 \u0915\u092e\u094d\u092a\u094d\u0932\u0940\u092e\u0947\u0902\u091f \u0915\u093e \u0907\u0902\u091f\u0930\u0938\u0947\u0915\u094d\u0936\u0928 \u0939\u092e\u0947\u0936\u093e \u0916\u093e\u0932\u0940 \u0938\u0947\u091f \u0939\u094b\u0924\u093e \u0939\u0948:<\/strong><\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">A\u2229A\u2032=\u2205A \u2229 A&#8217; = \u2205<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">A<\/span><span class=\"mbin\">\u2229<\/span><\/span><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">A<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mtight\">\u2032<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">\u2205<\/span><\/span><\/span><\/span><\/span><\/p>\n<h3 data-start=\"2341\" data-end=\"2385\"><strong data-start=\"2344\" data-end=\"2383\">\u00a0GATE (CSE\/IT) \u092e\u0947\u0902 \u0938\u0902\u092d\u093e\u0935\u093f\u0924 \u092a\u094d\u0930\u0936\u094d\u0928<\/strong><\/h3>\n<p data-start=\"2387\" data-end=\"2536\"><strong data-start=\"2390\" data-end=\"2397\">Q1:<\/strong> \u092f\u0926\u093f <strong data-start=\"2402\" data-end=\"2441\">U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}<\/strong> \u0914\u0930 <strong data-start=\"2445\" data-end=\"2469\">A = {2, 4, 6, 8, 10}<\/strong> \u0939\u094b, \u0924\u094b <strong data-start=\"2477\" data-end=\"2483\">A&#8217;<\/strong> \u0915\u094d\u092f\u093e \u0939\u094b\u0917\u093e?<br data-start=\"2494\" data-end=\"2497\" \/><strong data-start=\"2499\" data-end=\"2509\">\u0909\u0924\u094d\u0924\u0930:<\/strong> <strong data-start=\"2510\" data-end=\"2534\">A&#8217; = {1, 3, 5, 7, 9}<\/strong><\/p>\n<p data-start=\"2538\" data-end=\"2695\"><strong data-start=\"2541\" data-end=\"2548\">Q2:<\/strong> \u092f\u0926\u093f <strong data-start=\"2553\" data-end=\"2570\">A = {1, 2, 3}<\/strong>, <strong data-start=\"2572\" data-end=\"2589\">B = {3, 4, 5}<\/strong>, \u0914\u0930 <strong data-start=\"2594\" data-end=\"2620\">U = {1, 2, 3, 4, 5, 6}<\/strong>, \u0924\u094b <strong data-start=\"2625\" data-end=\"2637\">(A \u2229 B)\u2019<\/strong> \u0915\u094d\u092f\u093e \u0939\u094b\u0917\u093e?<br data-start=\"2648\" data-end=\"2651\" \/><strong data-start=\"2653\" data-end=\"2660\">\u0939\u0932:<\/strong><br data-start=\"2660\" data-end=\"2663\" \/>\u092a\u0939\u0932\u0947 \u0939\u092e <strong data-start=\"2671\" data-end=\"2680\">A \u2229 B<\/strong> \u0928\u093f\u0915\u093e\u0932\u0924\u0947 \u0939\u0948\u0902:<\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">A\u2229B={3}A \u2229 B = \\{3\\}<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">A<\/span><span class=\"mbin\">\u2229<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">B<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mopen\">{<\/span><span class=\"mord\">3<\/span><span class=\"mclose\">}<\/span><\/span><\/span><\/span><\/span><\/p>\n<p data-start=\"2718\" data-end=\"2766\">\u0905\u092c, <strong data-start=\"2722\" data-end=\"2764\">(A \u2229 B)\u2019 = U &#8211; {3} = {1, 2, 4, 5, 6}<\/strong><\/p>\n<h3 data-start=\"2773\" data-end=\"2806\"><strong data-start=\"2776\" data-end=\"2804\">\u00a0\u0928\u093f\u0937\u094d\u0915\u0930\u094d\u0937 (Conclusion)<\/strong><\/h3>\n<ul data-start=\"2807\" data-end=\"3105\">\n<li data-start=\"2807\" data-end=\"2862\"><strong data-start=\"2809\" data-end=\"2830\">\u092f\u0942\u0928\u093f\u0935\u0930\u094d\u0938\u0932 \u0938\u0947\u091f (U)<\/strong> \u0938\u092d\u0940 \u0924\u0924\u094d\u0935\u094b\u0902 \u0915\u094b \u0938\u092e\u093e\u0939\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948\u0964<\/li>\n<li data-start=\"2863\" data-end=\"2957\"><strong data-start=\"2865\" data-end=\"2899\">\u0915\u093f\u0938\u0940 \u0938\u0947\u091f A \u0915\u093e \u0915\u092e\u094d\u092a\u094d\u0932\u0940\u092e\u0947\u0902\u091f (A&#8217;)<\/strong> \u0935\u0947 \u0938\u092d\u0940 \u0924\u0924\u094d\u0935 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902 \u091c\u094b U \u092e\u0947\u0902 \u0939\u0948\u0902 \u0932\u0947\u0915\u093f\u0928 A \u092e\u0947\u0902 \u0928\u0939\u0940\u0902 \u0939\u0948\u0902\u0964<\/li>\n<li data-start=\"2958\" data-end=\"3018\"><strong data-start=\"2960\" data-end=\"2976\">\u0935\u0947\u0928 \u0921\u093e\u092f\u0917\u094d\u0930\u093e\u092e<\/strong> \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 \u0906\u0938\u093e\u0928\u0940 \u0938\u0947 \u0938\u092e\u091d\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948\u0964<\/li>\n<li data-start=\"3019\" data-end=\"3105\"><strong data-start=\"3021\" data-end=\"3103\">GATE \u092e\u0947\u0902 \u0905\u0915\u094d\u0938\u0930 \u0921\u093f \u092e\u0949\u0930\u094d\u0917\u0928 \u0915\u0947 \u0928\u093f\u092f\u092e \u0914\u0930 \u0915\u092e\u094d\u092a\u094d\u0932\u0940\u092e\u0947\u0902\u091f \u0938\u0947 \u091c\u0941\u0921\u093c\u0947 \u092a\u094d\u0930\u0936\u094d\u0928 \u092a\u0942\u091b\u0947 \u091c\u093e\u0924\u0947 \u0939\u0948\u0902\u0964<\/strong><\/li>\n<\/ul>\n<p data-start=\"3107\" data-end=\"3150\"><strong data-start=\"3110\" data-end=\"3125\">\u0905\u0917\u0932\u093e \u091f\u0949\u092a\u093f\u0915:<\/strong> Power Set \u0914\u0930 Subset<\/p>\n<p data-start=\"3152\" data-end=\"3199\" data-is-last-node=\"\" data-is-only-node=\"\"><strong data-start=\"3152\" data-end=\"3199\" data-is-last-node=\"\">\u0915\u094d\u092f\u093e \u0906\u092a\u0915\u094b \u0915\u094b\u0908 \u0914\u0930 \u0909\u0926\u093e\u0939\u0930\u0923 \u092f\u093e \u092a\u094d\u0930\u0936\u094d\u0928 \u091a\u093e\u0939\u093f\u090f?<\/strong><\/p>\n<h3 data-start=\"3152\" data-end=\"3199\"><a href=\"https:\/\/ncert.nic.in\/pdf\/publication\/exemplarproblem\/classXI\/mathematics(hindi)\/khep201.pdf\" target=\"_blank\" rel=\"noopener\">Day 01- Discrete Mathematics for gate in Hindi CSEIT- Concept of Universal set and Complement of set<\/a><\/h3>\n<h3 class=\"LC20lb MBeuO DKV0Md\"><a href=\"https:\/\/www2.cs.uh.edu\/~arjun\/courses\/ds\/DiscMaths4CompSc.pdf\" target=\"_blank\" rel=\"noopener\">Discrete Mathematics for Computer Science<\/a><\/h3>\n<h3 class=\"LC20lb MBeuO DKV0Md\"><a href=\"https:\/\/niamt.ac.in\/WriteReadData\/Mathematics%20(Discrete%20Structure).pdf\" target=\"_blank\" rel=\"noopener\">Mathematics (Discrete Structure).pdf<\/a><\/h3>\n<h3 class=\"LC20lb MBeuO DKV0Md\"><a href=\"https:\/\/sist.sathyabama.ac.in\/sist_coursematerial\/uploads\/SMT5201.pdf\" target=\"_blank\" rel=\"noopener\">UNIT \u2013 I \u2013 Set Theory \u2013 SMT5201<\/a><\/h3>\n<p>\u092f\u0939\u093e\u0901 <strong>Day 01 \u2013 Discrete Mathematics for GATE CSE\/IT (in Hindi)<\/strong> \u0915\u093e \u0938\u0902\u0915\u094d\u0937\u093f\u092a\u094d\u0924 \u0914\u0930 \u0938\u094d\u092a\u0937\u094d\u091f \u0928\u094b\u091f \u0939\u0948 \u091c\u093f\u0938\u092e\u0947\u0902 <strong>Universal Set<\/strong> \u0914\u0930 <strong>Complement of Set<\/strong> \u0915\u0940 <strong>\u0939\u093f\u0902\u0926\u0940 \u092e\u0947\u0902 \u0935\u094d\u092f\u093e\u0916\u094d\u092f\u093e<\/strong> \u0915\u0940 \u0917\u0908 \u0939\u0948\u0964<\/p>\n<hr \/>\n<h2>\ud83d\udcd8 <strong>Day 01 \u2013 Discrete Mathematics (\u0917\u0947\u091f CSE\/IT \u0915\u0947 \u0932\u093f\u090f)<\/strong><\/h2>\n<h3>\ud83c\udfaf \u091f\u0949\u092a\u093f\u0915: <strong>Universal Set (\u0938\u093e\u0930\u094d\u0935\u092d\u094c\u092e\u093f\u0915 \u0938\u092e\u0941\u091a\u094d\u091a\u092f)<\/strong> \u0914\u0930 <strong>Complement of Set (\u0938\u092e\u0941\u091a\u094d\u091a\u092f \u0915\u093e \u092a\u0942\u0930\u0915)<\/strong><\/h3>\n<hr \/>\n<h3>\ud83d\udd39 <strong>1. Universal Set (\u0938\u093e\u0930\u094d\u0935\u092d\u094c\u092e\u093f\u0915 \u0938\u092e\u0941\u091a\u094d\u091a\u092f)<\/strong><\/h3>\n<p><strong>\u092a\u0930\u093f\u092d\u093e\u0937\u093e:<\/strong><br \/>\n\u0935\u0939 \u0938\u092e\u0941\u091a\u094d\u091a\u092f \u091c\u093f\u0938\u092e\u0947\u0902 \u0909\u0938 \u0935\u093f\u0936\u0947\u0937 \u0938\u0902\u0926\u0930\u094d\u092d \u092e\u0947\u0902 \u092c\u093e\u0924 \u0915\u093f\u090f \u0917\u090f <strong>\u0938\u092d\u0940 \u0924\u0924\u094d\u0935 (elements)<\/strong> \u0936\u093e\u092e\u093f\u0932 \u0939\u094b\u0902, <strong>Universal Set<\/strong> \u0915\u0939\u0932\u093e\u0924\u093e \u0939\u0948\u0964<\/p>\n<p>\ud83d\udd39 \u0907\u0938\u0947 \u0905\u0915\u094d\u0938\u0930 <strong>U<\/strong> \u0938\u0947 \u0926\u0930\u094d\u0936\u093e\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964<br \/>\n\ud83d\udd39 \u092f\u0939 \u0938\u092d\u0940 \u0905\u0928\u094d\u092f \u0938\u092e\u0941\u091a\u094d\u091a\u092f\u094b\u0902 \u0915\u093e <strong>\u0938\u0941\u092a\u0930\u0938\u0947\u091f (Superset)<\/strong> \u0939\u094b\u0924\u093e \u0939\u0948\u0964<\/p>\n<h4>\ud83d\udccc <strong>\u0909\u0926\u093e\u0939\u0930\u0923:<\/strong><\/h4>\n<p>\u092e\u093e\u0928 \u0932\u0940\u091c\u093f\u090f, \u0939\u092e \u0915\u0947\u0935\u0932 1 \u0938\u0947 10 \u0924\u0915 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u0940 \u092c\u093e\u0924 \u0915\u0930 \u0930\u0939\u0947 \u0939\u0948\u0902\u0964<br \/>\n\u0924\u094b:<br \/>\n\ud83d\udc49 <strong>U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}<\/strong><\/p>\n<p>\u0905\u0917\u0930 A = {2, 4, 6}, \u0924\u094b A \u0915\u093e Universal Set \u0939\u094b\u0917\u093e U\u0964<\/p>\n<hr \/>\n<h3>\ud83d\udd39 <strong>2. Complement of a Set (\u0938\u092e\u0941\u091a\u094d\u091a\u092f \u0915\u093e \u092a\u0942\u0930\u0915)<\/strong><\/h3>\n<p><strong>\u092a\u0930\u093f\u092d\u093e\u0937\u093e:<\/strong><br \/>\n\u092f\u0926\u093f <strong>A<\/strong> \u0915\u094b\u0908 \u0938\u092e\u0941\u091a\u094d\u091a\u092f \u0939\u0948 \u0914\u0930 <strong>U<\/strong> \u0909\u0938\u0915\u093e Universal Set \u0939\u0948, \u0924\u094b <strong>A \u0915\u093e \u092a\u0942\u0930\u0915 (Complement)<\/strong> \u0935\u0939 \u0938\u092e\u0941\u091a\u094d\u091a\u092f \u0939\u094b\u0917\u093e \u091c\u093f\u0938\u092e\u0947\u0902 <strong>U \u0915\u0947 \u0935\u0947 \u0938\u092d\u0940 \u0924\u0924\u094d\u0935<\/strong> \u0939\u094b\u0902\u0917\u0947 \u091c\u094b <strong>A \u092e\u0947\u0902 \u0928\u0939\u0940\u0902<\/strong> \u0939\u0948\u0902\u0964<\/p>\n<p>\ud83d\udd39 \u0907\u0938\u0947 A&#8217; \u092f\u093e <strong>A\u0305 (A bar)<\/strong> \u0938\u0947 \u0926\u0930\u094d\u0936\u093e\u0924\u0947 \u0939\u0948\u0902\u0964<br \/>\n\ud83d\udd39 \u0917\u0923\u093f\u0924\u0940\u092f \u0930\u0942\u092a \u092e\u0947\u0902:<br \/>\n\ud83d\udc49 A&#8217; = U \u2013 A<\/p>\n<h4>\ud83d\udccc <strong>\u0909\u0926\u093e\u0939\u0930\u0923:<\/strong><\/h4>\n<p>U = {1, 2, 3, 4, 5, 6}<br \/>\nA = {2, 4, 6}<br \/>\n\u0924\u094b A&#8217; = {1, 3, 5}<\/p>\n<hr \/>\n<h3>\u2705 <strong>\u0928\u093f\u092f\u092e (Properties):<\/strong><\/h3>\n<table>\n<thead>\n<tr>\n<th>\u0928\u093f\u092f\u092e<\/th>\n<th>\u0935\u094d\u092f\u093e\u0916\u094d\u092f\u093e<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>(A&#8217;)&#8217; = A<\/td>\n<td>\u0921\u092c\u0932 \u092a\u0942\u0930\u0915 \u092b\u093f\u0930 \u0938\u0947 \u092e\u0942\u0932 \u0938\u092e\u0941\u091a\u094d\u091a\u092f \u092c\u0928\u0924\u093e \u0939\u0948<\/td>\n<\/tr>\n<tr>\n<td>U&#8217; = \u2205<\/td>\n<td>Universal Set \u0915\u093e \u092a\u0942\u0930\u0915 \u0916\u093e\u0932\u0940 \u0938\u092e\u0941\u091a\u094d\u091a\u092f \u0939\u094b\u0924\u093e \u0939\u0948<\/td>\n<\/tr>\n<tr>\n<td>\u2205&#8217; = U<\/td>\n<td>\u0916\u093e\u0932\u0940 \u0938\u092e\u0941\u091a\u094d\u091a\u092f \u0915\u093e \u092a\u0942\u0930\u0915 Universal Set \u0939\u094b\u0924\u093e \u0939\u0948<\/td>\n<\/tr>\n<tr>\n<td>A \u222a A&#8217; = U<\/td>\n<td>\u0938\u092e\u0941\u091a\u094d\u091a\u092f \u0914\u0930 \u0909\u0938\u0915\u093e \u092a\u0942\u0930\u0915 \u092e\u093f\u0932\u0915\u0930 Universal Set \u092c\u0928\u093e\u0924\u0947 \u0939\u0948\u0902<\/td>\n<\/tr>\n<tr>\n<td>A \u2229 A&#8217; = \u2205<\/td>\n<td>\u0938\u092e\u0941\u091a\u094d\u091a\u092f \u0914\u0930 \u0909\u0938\u0915\u093e \u092a\u0942\u0930\u0915 \u0906\u092a\u0938 \u092e\u0947\u0902 \u0915\u094b\u0908 \u0924\u0924\u094d\u0935 \u0938\u093e\u091d\u093e \u0928\u0939\u0940\u0902 \u0915\u0930\u0924\u0947<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<hr \/>\n<h3>\ud83c\udf93 <strong>GATE Exam \u092e\u0947\u0902 \u0915\u0948\u0938\u0947 \u092a\u0942\u091b\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948?<\/strong><\/h3>\n<p><strong>\u092a\u094d\u0930\u0936\u094d\u0928:<\/strong><br \/>\nU = {a, b, c, d, e}, A = {a, c, e}<br \/>\nA\u0305 \u0915\u094d\u092f\u093e \u0939\u094b\u0917\u093e?<\/p>\n<p><strong>\u0909\u0924\u094d\u0924\u0930:<\/strong><br \/>\nA\u0305 = U \u2013 A = {b, d}<\/p>\n<hr \/>\n<h3>\ud83d\udccc \u0938\u0941\u091d\u093e\u0935:<\/h3>\n<ul>\n<li><strong>Venn Diagram<\/strong> \u0938\u0947 \u0906\u092a \u0907\u0928 \u0915\u0949\u0928\u094d\u0938\u0947\u092a\u094d\u091f\u094d\u0938 \u0915\u094b \u0906\u0938\u093e\u0928\u0940 \u0938\u0947 \u0938\u092e\u091d \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964<\/li>\n<li>\u0906\u092a \u091a\u093e\u0939\u0947\u0902 \u0924\u094b \u092e\u0948\u0902 \u0907\u0938\u0915\u093e <strong>\u0939\u093f\u0902\u0926\u0940 \u0935\u0940\u0921\u093f\u092f\u094b \u0932\u093f\u0902\u0915, \u0928\u094b\u091f\u094d\u0938 PDF<\/strong> \u092f\u093e <strong>\u092a\u094d\u0930\u0948\u0915\u094d\u091f\u093f\u0938 \u0915\u094d\u0935\u093f\u091c\u093c<\/strong> \u092d\u0940 \u0926\u0947 \u0938\u0915\u0924\u093e \u0939\u0942\u0901\u0964<\/li>\n<\/ul>\n<hr \/>\n<p>\u0905\u0917\u0930 \u0906\u092a Day 02, 03, \u0906\u0926\u093f \u0915\u0947 \u0928\u094b\u091f\u094d\u0938 \u092f\u093e \u0905\u0928\u094d\u092f \u091f\u0949\u092a\u093f\u0915 \u091c\u0948\u0938\u0947 Power Set, Subset, \u092f\u093e Cartesian Product \u092d\u0940 \u091a\u093e\u0939\u0924\u0947 \u0939\u0948\u0902, \u0924\u094b \u092c\u0924\u093e\u0907\u090f \u2014 \u092e\u0948\u0902 \u0915\u094d\u0930\u092e \u0938\u0947 \u092c\u0928\u093e \u0926\u0942\u0901\u0964<\/p>\n<h3><a href=\"https:\/\/adityatekkali.edu.in\/autonomous\/AR16_IT.pdf\" target=\"_blank\" rel=\"noopener\">Day 01- Discrete Mathematics for gate in Hindi CSEIT- Concept of Universal set and Complement of set<\/a><\/h3>\n<div class=\"MjjYud\"><span id=\"fld_THE-aMu6GbCVseMPpfmOsA4_1\" class=\"oUAcPd\" data-csim=\"\"><\/span><\/p>\n<div class=\"wHYlTd Ww4FFb vt6azd tF2Cxc asEBEc\" lang=\"en\" data-eflcs=\"\" data-hveid=\"CCoQAA\" data-ved=\"2ahUKEwjLkLHirNSNAxWwSmwGHaW8A-YQFSgAegQIKhAA\">\n<div class=\"N54PNb BToiNc\" data-snc=\"NjN77\">\n<div class=\"kb0PBd A9Y9g jGGQ5e\" data-snf=\"x5WNvb\" data-snhf=\"0\">\n<div class=\"yuRUbf\">\n<div class=\"b8lM7\">\n<h3 class=\"LC20lb MBeuO DKV0Md\"><a href=\"https:\/\/aaa.iiita.ac.in\/senatepdf\/26th%20Senate%20Meeting.pdf\" target=\"_blank\" rel=\"noopener\">26th Meeting of the Senate (Annexure)<\/a><\/h3>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Day 01- Discrete Mathematics for gate in Hindi CSEIT- Concept of Universal set and Complement of set [fvplayer id=&#8221;275&#8243;] Day 01: \u0921\u093f\u0938\u094d\u0915\u094d\u0930\u0940\u091f \u092e\u0948\u0925\u092e\u0947\u091f\u093f\u0915\u094d\u0938 (Discrete Mathematics) &#8211; \u092f\u0942\u0928\u093f\u0935\u0930\u094d\u0938\u0932 \u0938\u0947\u091f \u0914\u0930 \u0915\u092e\u094d\u092a\u094d\u0932\u0940\u092e\u0947\u0902\u091f \u0911\u092b\u093c \u0938\u0947\u091f \u092f\u0939 \u091f\u0949\u092a\u093f\u0915 GATE (CSE\/IT) \u0915\u0947 \u0932\u093f\u090f \u092c\u0939\u0941\u0924 \u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u0939\u0948, \u0915\u094d\u092f\u094b\u0902\u0915\u093f \u0938\u0947\u091f \u0925\u094d\u092f\u094b\u0930\u0940 (Set Theory) \u0938\u0947 \u0905\u0915\u094d\u0938\u0930 \u092a\u094d\u0930\u0936\u094d\u0928 \u092a\u0942\u091b\u0947 \u091c\u093e\u0924\u0947 \u0939\u0948\u0902\u0964 \u00a0\u092f\u0942\u0928\u093f\u0935\u0930\u094d\u0938\u0932 \u0938\u0947\u091f (Universal [&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-3150","post","type-post","status-publish","format-standard","hentry","category-discrete-mathematics"],"_links":{"self":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts\/3150","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=3150"}],"version-history":[{"count":0,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts\/3150\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/media?parent=3150"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/categories?post=3150"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/tags?post=3150"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}