{"id":3121,"date":"2025-06-07T13:34:48","date_gmt":"2025-06-07T13:34:48","guid":{"rendered":"https:\/\/diznr.com\/?p=3121"},"modified":"2025-06-07T13:34:48","modified_gmt":"2025-06-07T13:34:48","slug":"previous-year-question-and-answer-in-hindi-gate-2016-set-theory-the-cardinality-of-the-set-power","status":"publish","type":"post","link":"https:\/\/www.reilsolar.com\/pdf\/previous-year-question-and-answer-in-hindi-gate-2016-set-theory-the-cardinality-of-the-set-power\/","title":{"rendered":"Previous year question and answer in Hindi &#8211; GATE 2025 Set Theory The cardinality of the power set."},"content":{"rendered":"<p>Previous year question and answer in Hindi &#8211; GATE 2025 Set Theory The cardinality of the power set.<\/p>\n<p>[fvplayer id=&#8221;263&#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]\">GATE \u092a\u0930\u0940\u0915\u094d\u0937\u093e \u0915\u0940 \u0924\u0948\u092f\u093e\u0930\u0940 \u092e\u0947\u0902 \u092a\u093f\u091b\u0932\u0947 \u0935\u0930\u094d\u0937\u094b\u0902 \u0915\u0947 \u092a\u094d\u0930\u0936\u094d\u0928 \u092a\u0924\u094d\u0930\u094b\u0902 \u0915\u093e \u0905\u092d\u094d\u092f\u093e\u0938 \u0905\u0924\u094d\u092f\u0902\u0924 \u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u0939\u0948, \u0915\u094d\u092f\u094b\u0902\u0915\u093f \u092f\u0939 \u092a\u0930\u0940\u0915\u094d\u0937\u093e \u0915\u0947 \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\u094b \u0938\u092e\u091d\u0928\u0947 \u092e\u0947\u0902 \u0938\u0939\u093e\u092f\u0924\u093e \u0915\u0930\u0924\u093e \u0939\u0948\u0964<\/span> <span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem]\">\u0935\u093f\u0936\u0947\u0937 \u0930\u0942\u092a \u0938\u0947, \u0938\u0947\u091f \u0925\u094d\u092f\u094b\u0930\u0940 \u092e\u0947\u0902 \u092a\u093e\u0935\u0930 \u0938\u0947\u091f \u0915\u0940 \u0915\u093e\u0930\u094d\u0921\u093f\u0928\u0947\u0932\u093f\u091f\u0940 (\u0938\u0924\u094d\u0924\u093e\u092e\u0942\u0932 \u0915\u093e \u092a\u0930\u093f\u092e\u093e\u0923) \u0938\u0947 \u0938\u0902\u092c\u0902\u0927\u093f\u0924 \u092a\u094d\u0930\u0936\u094d\u0928 \u0905\u0915\u094d\u0938\u0930 \u092a\u0942\u091b\u0947 \u091c\u093e\u0924\u0947 \u0939\u0948\u0902\u0964<\/span>\u200b<\/p>\n<p class=\"\" data-start=\"128\" data-end=\"157\"><strong data-start=\"128\" data-end=\"157\">\u092a\u093e\u0935\u0930 \u0938\u0947\u091f \u0915\u0940 \u0915\u093e\u0930\u094d\u0921\u093f\u0928\u0947\u0932\u093f\u091f\u0940:<\/strong><\/p>\n<p class=\"\" data-start=\"159\" data-end=\"278\"><span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem]\">\u092f\u0926\u093f \u0915\u093f\u0938\u0940 \u0938\u0947\u091f <span class=\"katex\"><span class=\"katex-mathml\">SS<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">S<\/span><\/span><\/span><\/span> \u092e\u0947\u0902 <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> \u0924\u0924\u094d\u0935 \u0939\u0948\u0902, \u0924\u094b \u0909\u0938\u0915\u0947 \u092a\u093e\u0935\u0930 \u0938\u0947\u091f <span class=\"katex\"><span class=\"katex-mathml\">P(S)P(S)<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">S<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span> \u092e\u0947\u0902 <span class=\"katex\"><span class=\"katex-mathml\">2n2^n<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">2<span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \u0909\u092a\u0938\u0947\u091f \u0939\u094b\u0902\u0917\u0947\u0964<\/span> <span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem]\">\u0909\u0926\u093e\u0939\u0930\u0923 \u0915\u0947 \u0932\u093f\u090f, \u092f\u0926\u093f <span class=\"katex\"><span class=\"katex-mathml\">S={a,b}S = \\{a, b\\}<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">S<\/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=\"mclose\">}<\/span><\/span><\/span><\/span> \u0939\u0948, \u0924\u094b <span class=\"katex\"><span class=\"katex-mathml\">SS<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">S<\/span><\/span><\/span><\/span> \u0915\u0947 \u092a\u093e\u0935\u0930 \u0938\u0947\u091f \u092e\u0947\u0902 <span class=\"katex\"><span class=\"katex-mathml\">22=42^2 = 4<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">2<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\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">4<\/span><\/span><\/span><\/span> \u0909\u092a\u0938\u0947\u091f \u0939\u094b\u0902\u0917\u0947: <span class=\"katex\"><span class=\"katex-mathml\">{},{a},{b},{a,b}\\{\\}, \\{a\\}, \\{b\\}, \\{a, b\\}<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mopen\">{<\/span><span class=\"mclose\">}<\/span><span class=\"mpunct\">,<\/span><span class=\"mopen\">{<\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mclose\">}<\/span><span class=\"mpunct\">,<\/span><span class=\"mopen\">{<\/span><span class=\"mord mathnormal\">b<\/span><span class=\"mclose\">}<\/span><span class=\"mpunct\">,<\/span><span class=\"mopen\">{<\/span><span class=\"mord mathnormal\">a<\/span><span class=\"mpunct\">,<\/span><span class=\"mord mathnormal\">b<\/span><span class=\"mclose\">}<\/span><\/span><\/span><\/span>\u0964<\/span>\u200b<\/p>\n<p class=\"\" data-start=\"280\" data-end=\"323\"><strong data-start=\"280\" data-end=\"323\">\u092a\u093f\u091b\u0932\u0947 \u0935\u0930\u094d\u0937\u094b\u0902 \u0915\u0947 \u092a\u094d\u0930\u0936\u094d\u0928 \u092a\u0924\u094d\u0930\u094b\u0902 \u0924\u0915 \u092a\u0939\u0941\u0902\u091a:<\/strong><\/p>\n<p class=\"\" data-start=\"325\" data-end=\"406\"><span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem]\">\u092a\u093f\u091b\u0932\u0947 \u0935\u0930\u094d\u0937\u094b\u0902 \u0915\u0947 GATE \u092a\u094d\u0930\u0936\u094d\u0928 \u092a\u0924\u094d\u0930\u094b\u0902 \u0915\u094b \u0921\u093e\u0909\u0928\u0932\u094b\u0921 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0938\u094d\u0930\u094b\u0924 \u0909\u092a\u092f\u094b\u0917\u0940 \u0939\u094b \u0938\u0915\u0924\u0947 \u0939\u0948\u0902:<\/span>\u200b<\/p>\n<ul data-start=\"408\" data-end=\"909\">\n<li class=\"\" data-start=\"408\" data-end=\"592\">\n<p class=\"\" data-start=\"410\" data-end=\"592\"><strong data-start=\"410\" data-end=\"470\">NPTEL (\u0928\u0947\u0936\u0928\u0932 \u092a\u094d\u0930\u094b\u0917\u094d\u0930\u093e\u092e \u0911\u0928 \u091f\u0947\u0915\u094d\u0928\u094b\u0932\u0949\u091c\u0940 \u090f\u0928\u094d\u0939\u093e\u0902\u0938\u094d\u0921 \u0932\u0930\u094d\u0928\u093f\u0902\u0917):<\/strong> <span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem]\">\u092f\u0939 \u092a\u094d\u0932\u0947\u091f\u092b\u093c\u0949\u0930\u094d\u092e MHRD \u0926\u094d\u0935\u093e\u0930\u093e IIT \u092e\u0926\u094d\u0930\u093e\u0938 \u0914\u0930 \u0905\u0928\u094d\u092f IITs \u0915\u0940 \u0938\u0939\u093e\u092f\u0924\u093e \u0938\u0947 \u0936\u0941\u0930\u0942 \u0915\u093f\u092f\u093e \u0917\u092f\u093e \u0939\u0948, \u091c\u0939\u093e\u0901 GATE \u0915\u0947 \u092a\u093f\u091b\u0932\u0947 \u0935\u0930\u094d\u0937\u094b\u0902 \u0915\u0947 \u092a\u094d\u0930\u0936\u094d\u0928 \u092a\u0924\u094d\u0930 \u0909\u092a\u0932\u092c\u094d\u0927 \u0939\u0948\u0902\u0964<\/span> \u200b<\/p>\n<\/li>\n<li class=\"\" data-start=\"594\" data-end=\"763\">\n<p class=\"\" data-start=\"596\" data-end=\"763\"><strong data-start=\"596\" data-end=\"637\">Previous Year Question Paper \u0935\u0947\u092c\u0938\u093e\u0907\u091f:<\/strong> <span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem]\">\u092f\u0939\u093e\u0901 GATE \u0915\u0947 \u0935\u093f\u0937\u092f\u0935\u093e\u0930 \u092a\u093f\u091b\u0932\u0947 \u0935\u0930\u094d\u0937\u094b\u0902 \u0915\u0947 \u092a\u094d\u0930\u0936\u094d\u0928 \u092a\u0924\u094d\u0930 \u0921\u093e\u0909\u0928\u0932\u094b\u0921 \u0915\u0947 \u0932\u093f\u090f \u0909\u092a\u0932\u092c\u094d\u0927 \u0939\u0948\u0902\u0964<\/span> \u200b<\/p>\n<\/li>\n<li class=\"\" data-start=\"594\" data-end=\"763\">\n<p class=\"\" data-start=\"596\" data-end=\"763\"><strong data-start=\"767\" data-end=\"783\">\u092c\u093f\u0939\u093e\u0930 \u0939\u0947\u0932\u094d\u092a:<\/strong> <span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem]\">\u0907\u0938 \u0935\u0947\u092c\u0938\u093e\u0907\u091f \u092a\u0930 2025 \u0938\u0947 2025 \u0924\u0915 \u0915\u0947 GATE \u092a\u094d\u0930\u0936\u094d\u0928 \u092a\u0924\u094d\u0930 \u0921\u093e\u0909\u0928\u0932\u094b\u0921 \u0915\u0947 \u0932\u093f\u090f \u0909\u092a\u0932\u092c\u094d\u0927 \u0939\u0948\u0902\u0964<\/span><\/p>\n<\/li>\n<\/ul>\n<p class=\"\" data-start=\"911\" data-end=\"931\"><strong data-start=\"911\" data-end=\"931\">\u0924\u0948\u092f\u093e\u0930\u0940 \u0915\u0947 \u0938\u0941\u091d\u093e\u0935:<\/strong><\/p>\n<ul data-start=\"933\" data-end=\"1240\">\n<li class=\"\" data-start=\"933\" data-end=\"1061\">\n<p class=\"\" data-start=\"935\" data-end=\"1061\"><strong data-start=\"935\" data-end=\"975\">\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:<\/strong> <span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem]\">\u092f\u0939 \u092a\u0930\u0940\u0915\u094d\u0937\u093e \u0915\u0947 \u092a\u0948\u091f\u0930\u094d\u0928 \u0914\u0930 \u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u0935\u093f\u0937\u092f\u094b\u0902 \u0915\u094b \u0938\u092e\u091d\u0928\u0947 \u092e\u0947\u0902 \u0938\u0939\u093e\u092f\u0915 \u0939\u094b\u0924\u093e \u0939\u0948\u0964<\/span>\u200b<\/p>\n<\/li>\n<li class=\"\" data-start=\"1063\" data-end=\"1240\">\n<p class=\"\" data-start=\"1065\" data-end=\"1240\"><strong data-start=\"1065\" data-end=\"1114\">\u092e\u0949\u0915 \u091f\u0947\u0938\u094d\u091f \u0914\u0930 \u0911\u0928\u0932\u093e\u0907\u0928 \u091f\u0947\u0938\u094d\u091f \u0938\u0940\u0930\u0940\u091c \u0915\u093e \u0932\u093e\u092d \u0909\u0920\u093e\u090f\u0902:<\/strong> <span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem]\">\u092f\u0939 \u0906\u092a\u0915\u0940 \u0917\u0924\u093f \u0914\u0930 \u0938\u091f\u0940\u0915\u0924\u093e \u092e\u0947\u0902 \u0938\u0941\u0927\u093e\u0930 \u0915\u0930\u0928\u0947 \u092e\u0947\u0902 \u092e\u0926\u0926 \u0915\u0930\u0947\u0917\u093e\u0964<\/span> \u200b<\/p>\n<\/li>\n<li class=\"\" data-start=\"1063\" data-end=\"1240\">\n<p class=\"\" data-start=\"1065\" data-end=\"1240\"><span class=\"relative -mx-px my-[-0.2rem] rounded px-px py-[0.2rem]\">\u0907\u0928 \u0938\u0902\u0938\u093e\u0927\u0928\u094b\u0902 \u0914\u0930 \u0938\u0941\u091d\u093e\u0935\u094b\u0902 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947, \u0906\u092a GATE 2025 \u0915\u0940 \u0924\u0948\u092f\u093e\u0930\u0940 \u092e\u0947\u0902 \u0938\u0947\u091f \u0925\u094d\u092f\u094b\u0930\u0940 \u0914\u0930 \u092a\u093e\u0935\u0930 \u0938\u0947\u091f \u0915\u0940 \u0915\u093e\u0930\u094d\u0921\u093f\u0928\u0947\u0932\u093f\u091f\u0940 \u091c\u0948\u0938\u0947 \u0935\u093f\u0937\u092f\u094b\u0902 \u092a\u0930 \u0905\u092a\u0928\u0940 \u092a\u0915\u0921\u093c \u092e\u091c\u092c\u0942\u0924 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964<\/span><\/p>\n<\/li>\n<\/ul>\n<h3><a href=\"https:\/\/www2.cs.uh.edu\/~arjun\/courses\/ds\/DiscMaths4CompSc.pdf\" target=\"_blank\" rel=\"noopener\">Previous year question and answer in Hindi &#8211; GATE 2025 Set Theory The cardinality of the power set.<\/a><\/h3>\n<p data-start=\"0\" data-end=\"168\">\u092f\u0939 \u0930\u0939\u093e <strong data-start=\"7\" data-end=\"38\">GATE 2025 (\u092f\u093e \u0915\u093f\u0938\u0940 \u092d\u0940 \u0935\u0930\u094d\u0937)<\/strong> \u0915\u0947 \u0932\u093f\u090f <strong data-start=\"46\" data-end=\"87\">Set Theory \u2013 Power Set \u0915\u0940 Cardinality<\/strong> \u0938\u0947 \u091c\u0941\u0921\u093c\u093e \u090f\u0915 \u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 <strong data-start=\"111\" data-end=\"143\">Previous Year Question (PYQ)<\/strong> \u0915\u093e <strong data-start=\"147\" data-end=\"167\">\u0939\u093f\u0902\u0926\u0940 \u092e\u0947\u0902 \u0938\u092e\u093e\u0927\u093e\u0928<\/strong>:<\/p>\n<hr data-start=\"170\" data-end=\"173\" \/>\n<h2 data-start=\"175\" data-end=\"203\">\ud83d\udcd8 <strong data-start=\"181\" data-end=\"203\">\u092a\u094d\u0930\u0936\u094d\u0928 (Question):<\/strong><\/h2>\n<p data-start=\"205\" data-end=\"335\">\u092f\u0926\u093f \u0915\u093f\u0938\u0940 \u0938\u0947\u091f <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> \u092e\u0947\u0902 <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> \u0924\u0924\u094d\u0924\u094d\u0935 (elements) \u0939\u0948\u0902, \u0924\u094b <strong data-start=\"264\" data-end=\"277\">Power Set<\/strong> <span class=\"katex\"><span class=\"katex-mathml\">P(A)P(A)<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span> \u0915\u0940 Cardinality (\u0924\u0924\u094d\u0924\u094d\u0935\u094b\u0902 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e) \u0915\u094d\u092f\u093e \u0939\u094b\u0917\u0940?<\/p>\n<p data-start=\"337\" data-end=\"407\"><strong data-start=\"337\" data-end=\"343\">A)<\/strong> <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><br data-start=\"351\" data-end=\"354\" \/><strong data-start=\"354\" data-end=\"360\">B)<\/strong> <span class=\"katex\"><span class=\"katex-mathml\">2n2n<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">2<\/span><span class=\"mord mathnormal\">n<\/span><\/span><\/span><\/span><br data-start=\"369\" data-end=\"372\" \/><strong data-start=\"372\" data-end=\"378\">C)<\/strong> <span class=\"katex\"><span class=\"katex-mathml\">2n2^n<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">2<span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><br data-start=\"388\" data-end=\"391\" \/><strong data-start=\"391\" data-end=\"397\">D)<\/strong> <span class=\"katex\"><span class=\"katex-mathml\">n2n^2<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">n<\/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\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<hr data-start=\"409\" data-end=\"412\" \/>\n<h2 data-start=\"414\" data-end=\"448\">\u2705 <strong data-start=\"419\" data-end=\"446\">\u0909\u0924\u094d\u0924\u0930 (Correct Answer):<\/strong><\/h2>\n<p data-start=\"449\" data-end=\"465\"><strong data-start=\"449\" data-end=\"465\">C) <span class=\"katex\"><span class=\"katex-mathml\">2n2^n<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">2<span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">n<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/strong><\/p>\n<hr data-start=\"467\" data-end=\"470\" \/>\n<h2 data-start=\"472\" data-end=\"512\">\ud83d\udd0d <strong data-start=\"478\" data-end=\"512\">\u0938\u092e\u091d\u093e\u0907\u090f (Explanation in Hindi):<\/strong><\/h2>\n<ul data-start=\"514\" data-end=\"757\">\n<li data-start=\"514\" data-end=\"757\">\n<p data-start=\"516\" data-end=\"687\">\u0915\u093f\u0938\u0940 \u0938\u0947\u091f <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> \u092e\u0947\u0902 \u092f\u0926\u093f <strong data-start=\"541\" data-end=\"552\"><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><\/strong> \u0924\u0924\u094d\u0924\u094d\u0935 \u0939\u0948\u0902, \u0924\u094b \u0909\u0938\u0915\u093e <strong data-start=\"573\" data-end=\"586\">Power Set<\/strong>, <span class=\"katex\"><span class=\"katex-mathml\">P(A)P(A)<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span>, \u0935\u0939 \u0938\u0947\u091f \u0939\u094b\u0924\u093e \u0939\u0948 \u091c\u093f\u0938\u092e\u0947\u0902 <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> \u0915\u0947 <strong data-start=\"633\" data-end=\"665\">\u0938\u092d\u0940 \u0938\u0902\u092d\u093e\u0935\u093f\u0924 subsets (\u0909\u092a-\u0938\u0947\u091f)<\/strong> \u0939\u094b\u0924\u0947 \u0939\u0948\u0902 \u2014 including:<\/p>\n<ul data-start=\"690\" data-end=\"757\">\n<li data-start=\"690\" data-end=\"710\">\n<p data-start=\"692\" data-end=\"710\"><strong data-start=\"692\" data-end=\"708\">\u2205 (null set)<\/strong><\/p>\n<\/li>\n<li data-start=\"713\" data-end=\"726\">\n<p data-start=\"715\" data-end=\"726\"><strong data-start=\"715\" data-end=\"726\">A \u0938\u094d\u0935\u092f\u0902<\/strong><\/p>\n<\/li>\n<li data-start=\"729\" data-end=\"757\">\n<p data-start=\"731\" data-end=\"757\">\u0914\u0930 \u092c\u0940\u091a \u0915\u0947 \u0938\u092d\u0940 combinations<\/p>\n<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<hr data-start=\"759\" data-end=\"762\" \/>\n<h3 data-start=\"764\" data-end=\"791\">\ud83d\udccc <strong data-start=\"771\" data-end=\"791\">\u0938\u0942\u0924\u094d\u0930 (Formula):<\/strong><\/h3>\n<p data-start=\"798\" data-end=\"813\">|P(A)| = 2^n<br \/>\n]<\/p>\n<p data-start=\"815\" data-end=\"875\">\u091c\u0939\u093e\u0901 <span class=\"katex\"><span class=\"katex-mathml\">n=\u2223A\u2223n = |A|<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">n<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mord\">\u2223<\/span><\/span><\/span><\/span> (\u092f\u093e\u0928\u0940 \u0938\u0947\u091f <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> \u092e\u0947\u0902 \u0924\u0924\u094d\u0924\u094d\u0935\u094b\u0902 \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e)<\/p>\n<hr data-start=\"877\" data-end=\"880\" \/>\n<h3 data-start=\"882\" data-end=\"900\">\ud83e\udde0 <strong data-start=\"889\" data-end=\"900\">\u0909\u0926\u093e\u0939\u0930\u0923:<\/strong><\/h3>\n<p data-start=\"902\" data-end=\"907\">\u0905\u0917\u0930<\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">A={1,2}\u21d2n=2A = \\{1, 2\\} \\Rightarrow n = 2<\/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=\"mopen\">{<\/span><span class=\"mord\">1<\/span><span class=\"mpunct\">,<\/span><span class=\"mord\">2<\/span><span class=\"mclose\">}<\/span><span class=\"mrel\">\u21d2<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">n<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">2<\/span><\/span><\/span><\/span><\/span><\/p>\n<p data-start=\"946\" data-end=\"950\">\u0924\u094b<\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">P(A)={\u2205,{1},{2},{1,2}}\u21d2\u2223P(A)\u2223=4=22P(A) = \\{\\emptyset, \\{1\\}, \\{2\\}, \\{1, 2\\}\\} \\Rightarrow |P(A)| = 4 = 2^2<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mopen\">{<\/span><span class=\"mord\">\u2205<\/span><span class=\"mpunct\">,<\/span><span class=\"mopen\">{<\/span><span class=\"mord\">1<\/span><span class=\"mclose\">}<\/span><span class=\"mpunct\">,<\/span><span class=\"mopen\">{<\/span><span class=\"mord\">2<\/span><span class=\"mclose\">}<\/span><span class=\"mpunct\">,<\/span><span class=\"mopen\">{<\/span><span class=\"mord\">1<\/span><span class=\"mpunct\">,<\/span><span class=\"mord\">2<\/span><span class=\"mclose\">}}<\/span><span class=\"mrel\">\u21d2<\/span><\/span><span class=\"base\"><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">P<\/span><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mclose\">)<\/span><span class=\"mord\">\u2223<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">4<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">2<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\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n<hr data-start=\"1032\" data-end=\"1035\" \/>\n<h2 data-start=\"1037\" data-end=\"1072\">\ud83d\udca1 <strong data-start=\"1043\" data-end=\"1072\">\u0938\u093f\u0926\u094d\u0927\u093e\u0902\u0924 (Concept Recap):<\/strong><\/h2>\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=\"1074\" data-end=\"1414\">\n<thead data-start=\"1074\" data-end=\"1120\">\n<tr data-start=\"1074\" data-end=\"1120\">\n<th data-start=\"1074\" data-end=\"1095\" data-col-size=\"sm\">\u092e\u0942\u0932 \u0938\u0947\u091f \u092e\u0947\u0902 \u0924\u0924\u094d\u0924\u094d\u0935<\/th>\n<th data-start=\"1095\" data-end=\"1120\" data-col-size=\"sm\">Power Set \u092e\u0947\u0902 subsets<\/th>\n<\/tr>\n<\/thead>\n<tbody data-start=\"1170\" data-end=\"1414\">\n<tr data-start=\"1170\" data-end=\"1218\">\n<td data-start=\"1170\" data-end=\"1192\" data-col-size=\"sm\">0<\/td>\n<td data-col-size=\"sm\" data-start=\"1192\" data-end=\"1218\">1 (= <span class=\"katex\"><span class=\"katex-mathml\">202^0<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">2<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\">0<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/td>\n<\/tr>\n<tr data-start=\"1219\" data-end=\"1267\">\n<td data-start=\"1219\" data-end=\"1241\" data-col-size=\"sm\">1<\/td>\n<td data-col-size=\"sm\" data-start=\"1241\" data-end=\"1267\">2 (= <span class=\"katex\"><span class=\"katex-mathml\">212^1<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">2<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\">1<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/td>\n<\/tr>\n<tr data-start=\"1268\" data-end=\"1316\">\n<td data-start=\"1268\" data-end=\"1290\" data-col-size=\"sm\">2<\/td>\n<td data-start=\"1290\" data-end=\"1316\" data-col-size=\"sm\">4 (= <span class=\"katex\"><span class=\"katex-mathml\">222^2<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">2<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\">2<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/td>\n<\/tr>\n<tr data-start=\"1317\" data-end=\"1365\">\n<td data-start=\"1317\" data-end=\"1339\" data-col-size=\"sm\">3<\/td>\n<td data-col-size=\"sm\" data-start=\"1339\" data-end=\"1365\">8 (= <span class=\"katex\"><span class=\"katex-mathml\">232^3<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">2<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\">3<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>)<\/td>\n<\/tr>\n<tr data-start=\"1366\" data-end=\"1414\">\n<td data-start=\"1366\" data-end=\"1388\" data-col-size=\"sm\">&#8230;<\/td>\n<td data-start=\"1388\" data-end=\"1414\" data-col-size=\"sm\">&#8230;<\/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=\"1416\" data-end=\"1419\" \/>\n<h2 data-start=\"1421\" data-end=\"1453\">\ud83d\udcdd <strong data-start=\"1427\" data-end=\"1453\">\u0928\u093f\u0937\u094d\u0915\u0930\u094d\u0937 (Conclusion):<\/strong><\/h2>\n<p data-start=\"1455\" data-end=\"1587\">\u092f\u0926\u093f GATE \u092f\u093e \u0915\u093f\u0938\u0940 \u0905\u0928\u094d\u092f \u092a\u094d\u0930\u0924\u093f\u092f\u094b\u0917\u0940 \u092a\u0930\u0940\u0915\u094d\u0937\u093e \u092e\u0947\u0902 Power Set \u0915\u0940 Cardinality \u092a\u0942\u091b\u0940 \u091c\u093e\u090f, \u0914\u0930 \u092e\u0942\u0932 \u0938\u0947\u091f \u092e\u0947\u0902 <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> \u0924\u0924\u094d\u0924\u094d\u0935 \u0939\u0948\u0902, \u0924\u094b \u0938\u0939\u0940 \u0909\u0924\u094d\u0924\u0930 \u0939\u094b\u0917\u093e:<\/p>\n<p data-start=\"1594\" data-end=\"1608\">\\boxed{2^n}<br \/>\n]<\/p>\n<hr data-start=\"1610\" data-end=\"1613\" \/>\n<p data-start=\"1615\" data-end=\"1633\">\u0905\u0917\u0930 \u0906\u092a \u091a\u093e\u0939\u0947\u0902, \u092e\u0948\u0902:<\/p>\n<ul data-start=\"1634\" data-end=\"1761\">\n<li data-start=\"1634\" data-end=\"1676\">\n<p data-start=\"1636\" data-end=\"1676\">\u0907\u0938\u0938\u0947 \u091c\u0941\u0921\u093c\u0947 \u0914\u0930 \u092d\u0940 GATE PYQs \u0932\u093e \u0938\u0915\u0924\u093e \u0939\u0942\u0901<\/p>\n<\/li>\n<li data-start=\"1677\" data-end=\"1730\">\n<p data-start=\"1679\" data-end=\"1730\">\u0907\u0938\u0940 \u0935\u093f\u0937\u092f \u092a\u0930 \u090f\u0915 Hindi short notes PDF \u092c\u0928\u093e \u0938\u0915\u0924\u093e \u0939\u0942\u0901<\/p>\n<\/li>\n<li data-start=\"1731\" data-end=\"1761\">\n<p data-start=\"1733\" data-end=\"1761\">\u092f\u093e Practice MCQs \u0926\u0947 \u0938\u0915\u0924\u093e \u0939\u0942\u0901<\/p>\n<\/li>\n<\/ul>\n<p data-start=\"1763\" data-end=\"1783\" data-is-last-node=\"\" data-is-only-node=\"\">\u092c\u0924\u093e\u0907\u090f \u0915\u0948\u0938\u0947 \u092e\u0926\u0926 \u0915\u0930\u0942\u0901?<\/p>\n<h3 data-start=\"1763\" data-end=\"1783\"><a href=\"https:\/\/www.ncert.nic.in\/pdf\/NCF_for_Foundational_Stage_20_October_2022.pdf\" target=\"_blank\" rel=\"noopener\">Previous year question and answer in Hindi &#8211; GATE 2025 Set Theory The cardinality of the power set.<\/a><\/h3>\n","protected":false},"excerpt":{"rendered":"<p>Previous year question and answer in Hindi &#8211; GATE 2025 Set Theory The cardinality of the power set. [fvplayer id=&#8221;263&#8243;] \u200bGATE \u092a\u0930\u0940\u0915\u094d\u0937\u093e \u0915\u0940 \u0924\u0948\u092f\u093e\u0930\u0940 \u092e\u0947\u0902 \u092a\u093f\u091b\u0932\u0947 \u0935\u0930\u094d\u0937\u094b\u0902 \u0915\u0947 \u092a\u094d\u0930\u0936\u094d\u0928 \u092a\u0924\u094d\u0930\u094b\u0902 \u0915\u093e \u0905\u092d\u094d\u092f\u093e\u0938 \u0905\u0924\u094d\u092f\u0902\u0924 \u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u0939\u0948, \u0915\u094d\u092f\u094b\u0902\u0915\u093f \u092f\u0939 \u092a\u0930\u0940\u0915\u094d\u0937\u093e \u0915\u0947 \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\u094b \u0938\u092e\u091d\u0928\u0947 \u092e\u0947\u0902 \u0938\u0939\u093e\u092f\u0924\u093e \u0915\u0930\u0924\u093e \u0939\u0948\u0964 \u0935\u093f\u0936\u0947\u0937 \u0930\u0942\u092a \u0938\u0947, \u0938\u0947\u091f \u0925\u094d\u092f\u094b\u0930\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-3121","post","type-post","status-publish","format-standard","hentry","category-discrete-mathematics"],"_links":{"self":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts\/3121","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=3121"}],"version-history":[{"count":0,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts\/3121\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/media?parent=3121"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/categories?post=3121"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/tags?post=3121"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}