{"id":3406,"date":"2025-06-06T12:39:00","date_gmt":"2025-06-06T12:39:00","guid":{"rendered":"https:\/\/diznr.com\/?p=3406"},"modified":"2025-06-06T12:39:00","modified_gmt":"2025-06-06T12:39:00","slug":"general-aptitude-for-gate-cseit-set-theory-maxima-minima-using-short-trick-method-1-part","status":"publish","type":"post","link":"https:\/\/www.reilsolar.com\/pdf\/general-aptitude-for-gate-cseit-set-theory-maxima-minima-using-short-trick-method-1-part\/","title":{"rendered":"General Aptitude For Gate CSEIT &#8211; Set Theory Maxima-Minima Using Short Trick Method Part 1."},"content":{"rendered":"<p>General Aptitude For Gate CSEIT &#8211; Set Theory Maxima-Minima Using Short Trick Method Part 1.<\/p>\n<p>[fvplayer id=&#8221;391&#8243;]<\/p>\n<h3 data-start=\"0\" data-end=\"70\"><strong data-start=\"4\" data-end=\"68\">\u00a0Set Theory \u2013 Maxima &amp; Minima Short Tricks for GATE CSE\/IT<\/strong><\/h3>\n<p data-start=\"72\" data-end=\"245\">Set Theory is an important topic in <strong data-start=\"108\" data-end=\"138\">GATE Computer Science &amp; IT<\/strong>. Questions related to <strong data-start=\"161\" data-end=\"182\">Maxima and Minima<\/strong> of sets often appear in <strong data-start=\"207\" data-end=\"242\">Aptitude &amp; Discrete Mathematics<\/strong>.<\/p>\n<h3 data-start=\"252\" data-end=\"295\"><strong data-start=\"255\" data-end=\"293\">\u00a01. Basic Formulas of Set Theory<\/strong><\/h3>\n<p data-start=\"297\" data-end=\"352\">For two sets <strong data-start=\"310\" data-end=\"315\">A<\/strong> and <strong data-start=\"320\" data-end=\"325\">B<\/strong>:<br data-start=\"326\" data-end=\"329\" \/><strong data-start=\"332\" data-end=\"350\">Union Formula:<\/strong><\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">\u2223A\u222aB\u2223=\u2223A\u2223+\u2223B\u2223\u2212\u2223A\u2229B\u2223|A \\cup B| = |A| + |B| &#8211; |A \\cap B|<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mbin\">\u222a<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">B<\/span><span class=\"mord\">\u2223<\/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 class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">B<\/span><span class=\"mord\">\u2223<\/span><span class=\"mbin\">\u2212<\/span><\/span><span class=\"base\"><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mbin\">\u2229<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">B<\/span><span class=\"mord\">\u2223<\/span><\/span><\/span><\/span><\/span><\/p>\n<p data-start=\"398\" data-end=\"428\"><strong data-start=\"401\" data-end=\"426\">Intersection Formula:<\/strong><\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">\u2223A\u2229B\u2223=\u2223A\u2223+\u2223B\u2223\u2212\u2223A\u222aB\u2223|A \\cap B| = |A| + |B| &#8211; |A \\cup B|<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mbin\">\u2229<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">B<\/span><span class=\"mord\">\u2223<\/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 class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">B<\/span><span class=\"mord\">\u2223<\/span><span class=\"mbin\">\u2212<\/span><\/span><span class=\"base\"><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mbin\">\u222a<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">B<\/span><span class=\"mord\">\u2223<\/span><\/span><\/span><\/span><\/span><\/p>\n<p data-start=\"474\" data-end=\"502\"><strong data-start=\"477\" data-end=\"500\">Complement Formula:<\/strong><\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">\u2223Ac\u2223=U\u2212\u2223A\u2223|A^c| = U &#8211; |A|<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">\u2223<\/span><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 mathnormal mtight\">c<\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mord\">\u2223<\/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\">\u2223<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mord\">\u2223<\/span><\/span><\/span><\/span><\/span><\/p>\n<p data-start=\"527\" data-end=\"563\">(where <strong data-start=\"534\" data-end=\"539\">U<\/strong> is the universal set)<\/p>\n<p data-start=\"565\" data-end=\"599\"><strong data-start=\"568\" data-end=\"597\">For Three Sets (A, B, C):<\/strong><\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">\u2223A\u222aB\u222aC\u2223=\u2223A\u2223+\u2223B\u2223+\u2223C\u2223\u2212\u2223A\u2229B\u2223\u2212\u2223B\u2229C\u2223\u2212\u2223C\u2229A\u2223+\u2223A\u2229B\u2229C\u2223|A \\cup B \\cup C| = |A| + |B| + |C| &#8211; |A \\cap B| &#8211; |B \\cap C| &#8211; |C \\cap A| + |A \\cap B \\cap C|<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mbin\">\u222a<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">B<\/span><span class=\"mbin\">\u222a<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">C<\/span><span class=\"mord\">\u2223<\/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 class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">B<\/span><span class=\"mord\">\u2223<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">C<\/span><span class=\"mord\">\u2223<\/span><span class=\"mbin\">\u2212<\/span><\/span><span class=\"base\"><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mbin\">\u2229<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">B<\/span><span class=\"mord\">\u2223<\/span><span class=\"mbin\">\u2212<\/span><\/span><span class=\"base\"><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">B<\/span><span class=\"mbin\">\u2229<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">C<\/span><span class=\"mord\">\u2223<\/span><span class=\"mbin\">\u2212<\/span><\/span><span class=\"base\"><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">C<\/span><span class=\"mbin\">\u2229<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">A<\/span><span class=\"mord\">\u2223<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mbin\">\u2229<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">B<\/span><span class=\"mbin\">\u2229<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">C<\/span><span class=\"mord\">\u2223<\/span><\/span><\/span><\/span><\/span><\/p>\n<h3 data-start=\"709\" data-end=\"762\"><strong data-start=\"712\" data-end=\"760\">\u00a02. Maxima and Minima Tricks in Set Theory<\/strong><\/h3>\n<p data-start=\"764\" data-end=\"903\"><strong data-start=\"767\" data-end=\"811\">Case 1: Finding Maximum Value of |A \u2229 B|<\/strong><br data-start=\"811\" data-end=\"814\" \/>\u00a0The maximum value of <strong data-start=\"838\" data-end=\"849\">|A \u2229 B|<\/strong> occurs when one set is completely inside the other.<\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">max\u2061(\u2223A\u2229B\u2223)=min\u2061(\u2223A\u2223,\u2223B\u2223)\\max(|A \\cap B|) = \\min(|A|, |B|)<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mop\">max<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mbin\">\u2229<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">B<\/span><span class=\"mord\">\u2223<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mop\">min<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mord\">\u2223<\/span><span class=\"mpunct\">,<\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">B<\/span><span class=\"mord\">\u2223<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/p>\n<p data-start=\"947\" data-end=\"1070\"><strong data-start=\"950\" data-end=\"994\">Case 2: Finding Minimum Value of |A \u2229 B|<\/strong><br data-start=\"994\" data-end=\"997\" \/>\u00a0The minimum value of <strong data-start=\"1021\" data-end=\"1032\">|A \u2229 B|<\/strong> occurs when both sets are disjoint.<\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">min\u2061(\u2223A\u2229B\u2223)=0\\min(|A \\cap B|) = 0<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mop\">min<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mbin\">\u2229<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">B<\/span><span class=\"mord\">\u2223<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/span><\/p>\n<p data-start=\"1101\" data-end=\"1238\"><strong data-start=\"1104\" data-end=\"1148\">Case 3: Finding Maximum Value of |A \u222a B|<\/strong><br data-start=\"1148\" data-end=\"1151\" \/>\u00a0The maximum value of <strong data-start=\"1175\" data-end=\"1186\">|A \u222a B|<\/strong> occurs when the two sets have no common elements.<\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">max\u2061(\u2223A\u222aB\u2223)=\u2223A\u2223+\u2223B\u2223\\max(|A \\cup B|) = |A| + |B|<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mop\">max<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mbin\">\u222a<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">B<\/span><span class=\"mord\">\u2223<\/span><span class=\"mclose\">)<\/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 class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">B<\/span><span class=\"mord\">\u2223<\/span><\/span><\/span><\/span><\/span><\/p>\n<p data-start=\"1277\" data-end=\"1416\"><strong data-start=\"1280\" data-end=\"1324\">Case 4: Finding Minimum Value of |A \u222a B|<\/strong><br data-start=\"1324\" data-end=\"1327\" \/>\u00a0The minimum value of <strong data-start=\"1351\" data-end=\"1362\">|A \u222a B|<\/strong> occurs when one set is completely inside the other.<\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">min\u2061(\u2223A\u222aB\u2223)=max\u2061(\u2223A\u2223,\u2223B\u2223)\\min(|A \\cup B|) = \\max(|A|, |B|)<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mop\">min<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mbin\">\u222a<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">B<\/span><span class=\"mord\">\u2223<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mop\">max<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mord\">\u2223<\/span><span class=\"mpunct\">,<\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">B<\/span><span class=\"mord\">\u2223<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/p>\n<h3 data-start=\"1465\" data-end=\"1505\"><strong data-start=\"1468\" data-end=\"1503\">\u00a03. Shortcut Example Question<\/strong><\/h3>\n<h3 data-start=\"1507\" data-end=\"1529\"><strong data-start=\"1511\" data-end=\"1527\">\u00a0Question:<\/strong><\/h3>\n<p data-start=\"1530\" data-end=\"1627\">If <strong data-start=\"1533\" data-end=\"1545\">|A| = 10<\/strong> and <strong data-start=\"1550\" data-end=\"1561\">|B| = 7<\/strong>, then what is the <strong data-start=\"1580\" data-end=\"1603\">maximum and minimum<\/strong> value of <strong data-start=\"1613\" data-end=\"1624\">|A \u2229 B|<\/strong>?<\/p>\n<h3 data-start=\"1629\" data-end=\"1650\"><strong data-start=\"1633\" data-end=\"1648\">\u00a0Solution:<\/strong><\/h3>\n<p data-start=\"1651\" data-end=\"1703\"><strong data-start=\"1654\" data-end=\"1665\">Maximum<\/strong>: When <strong data-start=\"1672\" data-end=\"1700\">B is completely inside A<\/strong>,<\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">max\u2061(\u2223A\u2229B\u2223)=min\u2061(10,7)=7\\max(|A \\cap B|) = \\min(10, 7) = 7<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mop\">max<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mbin\">\u2229<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">B<\/span><span class=\"mord\">\u2223<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mop\">min<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">10<\/span><span class=\"mpunct\">,<\/span><span class=\"mord\">7<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">7<\/span><\/span><\/span><\/span><\/span><\/p>\n<p data-start=\"1748\" data-end=\"1796\"><strong data-start=\"1751\" data-end=\"1762\">Minimum<\/strong>: When <strong data-start=\"1769\" data-end=\"1793\">A and B are disjoint<\/strong>,<\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">min\u2061(\u2223A\u2229B\u2223)=0\\min(|A \\cap B|) = 0<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mop\">min<\/span><span class=\"mopen\">(<\/span><span class=\"mord\">\u2223<\/span><span class=\"mord mathnormal\">A<\/span><span class=\"mbin\">\u2229<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">B<\/span><span class=\"mord\">\u2223<\/span><span class=\"mclose\">)<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mord\">0<\/span><\/span><\/span><\/span><\/span><\/p>\n<p data-start=\"1827\" data-end=\"1880\"><strong data-start=\"1830\" data-end=\"1847\">Final Answer:<\/strong> \u00a0<strong data-start=\"1850\" data-end=\"1878\">Maximum = 7, Minimum = 0<\/strong><\/p>\n<h3 data-start=\"1887\" data-end=\"1926\"><strong data-start=\"1890\" data-end=\"1924\">\u00a04. Short Tricks to Remember<\/strong><\/h3>\n<p data-start=\"1927\" data-end=\"1960\"><strong data-start=\"1929\" data-end=\"1958\">For Intersection (A \u2229 B):<\/strong><\/p>\n<ul data-start=\"1964\" data-end=\"2027\">\n<li data-start=\"1964\" data-end=\"1994\"><strong data-start=\"1966\" data-end=\"1992\">Max = Smaller Set Size<\/strong><\/li>\n<li data-start=\"1998\" data-end=\"2027\"><strong data-start=\"2000\" data-end=\"2011\">Min = 0<\/strong> (if disjoint)<\/li>\n<\/ul>\n<p data-start=\"2029\" data-end=\"2055\"><strong data-start=\"2031\" data-end=\"2053\">For Union (A \u222a B):<\/strong><\/p>\n<ul data-start=\"2059\" data-end=\"2127\">\n<li data-start=\"2059\" data-end=\"2094\"><strong data-start=\"2061\" data-end=\"2092\">Max = Sum of Both Set Sizes<\/strong><\/li>\n<li data-start=\"2098\" data-end=\"2127\"><strong data-start=\"2100\" data-end=\"2125\">Min = Larger Set Size<\/strong><\/li>\n<\/ul>\n<h3 data-start=\"2134\" data-end=\"2157\"><strong data-start=\"2138\" data-end=\"2155\">\u00a0Conclusion<\/strong><\/h3>\n<p data-start=\"2158\" data-end=\"2356\" data-is-last-node=\"\" data-is-only-node=\"\">These <strong data-start=\"2164\" data-end=\"2180\">short tricks<\/strong> help solve <strong data-start=\"2192\" data-end=\"2220\">Set Theory Maxima-Minima<\/strong> problems quickly in <strong data-start=\"2241\" data-end=\"2283\">GATE, SSC, and other competitive exams<\/strong>. Would you like me to add more <strong data-start=\"2315\" data-end=\"2352\">practice questions with solutions<\/strong>?<\/p>\n<h3 data-start=\"2158\" data-end=\"2356\"><a href=\"https:\/\/www.bennett.edu.in\/wp-content\/uploads\/2022\/11\/BTech-Detailed-Syllabus_2022_compressed-1.pdf\" target=\"_blank\" rel=\"noopener\">General Aptitude For Gate CSEIT &#8211; Set Theory Maxima-Minima Using Short Trick Method Part 1.<\/a><\/h3>\n<h3 class=\"LC20lb MBeuO DKV0Md\"><a href=\"https:\/\/mrcet.com\/downloads\/B.Tech%20eBooks%20&amp;%20Online%20Video%20Lectures\/B.Tech%20eBooks\/GATE%20MECHANICAL%20WEB%20LINKS.pdf\" target=\"_blank\" rel=\"noopener\">GATE Mechanical Resource<\/a><\/h3>\n<article class=\"text-token-text-primary w-full\" dir=\"auto\" data-testid=\"conversation-turn-66\" data-scroll-anchor=\"true\">\n<div class=\"text-base my-auto mx-auto py-5 [--thread-content-margin:--spacing(4)] @[37rem]:[--thread-content-margin:--spacing(6)] @[72rem]:[--thread-content-margin:--spacing(16)] px-(--thread-content-margin)\">\n<div class=\"[--thread-content-max-width:32rem] @[34rem]:[--thread-content-max-width:40rem] @[64rem]:[--thread-content-max-width:48rem] mx-auto flex max-w-(--thread-content-max-width) flex-1 text-base gap-4 md:gap-5 lg:gap-6 group\/turn-messages focus-visible:outline-hidden\">\n<div class=\"group\/conversation-turn relative flex w-full min-w-0 flex-col agent-turn\">\n<div class=\"relative flex-col gap-1 md:gap-3\">\n<div class=\"flex max-w-full flex-col grow\">\n<div class=\"min-h-8 text-message relative flex w-full flex-col items-end gap-2 text-start break-words whitespace-normal [.text-message+&amp;]:mt-5\" dir=\"auto\" data-message-author-role=\"assistant\" data-message-id=\"2d6985a9-657e-42b6-9c73-f98da3f2a2e4\" data-message-model-slug=\"gpt-4o\">\n<div class=\"flex w-full flex-col gap-1 empty:hidden first:pt-[3px]\">\n<div class=\"markdown prose dark:prose-invert w-full break-words light\">\n<p data-start=\"0\" data-end=\"67\">Here&#8217;s a structured guide for a <strong data-start=\"32\" data-end=\"63\">video lecture or study note<\/strong> on:<\/p>\n<hr data-start=\"69\" data-end=\"72\" \/>\n<h2 data-start=\"74\" data-end=\"118\">\ud83c\udf93 <strong data-start=\"80\" data-end=\"116\">General Aptitude for GATE CSE\/IT<\/strong><\/h2>\n<h3 data-start=\"119\" data-end=\"180\"><strong data-start=\"123\" data-end=\"180\">Set Theory + Maxima-Minima Using Short Trick \u2013 Part 1<\/strong><\/h3>\n<hr data-start=\"182\" data-end=\"185\" \/>\n<h3 data-start=\"187\" data-end=\"244\">\ud83d\udd39 <strong data-start=\"194\" data-end=\"244\">\ud83d\udccd Part A: Set Theory \u2013 GATE-Oriented Concepts<\/strong><\/h3>\n<h4 data-start=\"246\" data-end=\"266\">\u2705 Key Concepts:<\/h4>\n<ul data-start=\"267\" data-end=\"440\">\n<li data-start=\"267\" data-end=\"323\">\n<p data-start=\"269\" data-end=\"323\"><strong data-start=\"269\" data-end=\"285\">Set Notation<\/strong>: A, B, C are sets. Universal Set: U<\/p>\n<\/li>\n<li data-start=\"324\" data-end=\"440\">\n<p data-start=\"326\" data-end=\"343\"><strong data-start=\"326\" data-end=\"340\">Operations<\/strong>:<\/p>\n<ul data-start=\"346\" data-end=\"440\">\n<li data-start=\"346\" data-end=\"362\">\n<p data-start=\"348\" data-end=\"362\">Union: A \u222a B<\/p>\n<\/li>\n<li data-start=\"365\" data-end=\"388\">\n<p data-start=\"367\" data-end=\"388\">Intersection: A \u2229 B<\/p>\n<\/li>\n<li data-start=\"391\" data-end=\"418\">\n<p data-start=\"393\" data-end=\"418\">Complement: A\u2032 or U \u2212 A<\/p>\n<\/li>\n<li data-start=\"421\" data-end=\"440\">\n<p data-start=\"423\" data-end=\"440\">Difference: A \u2212 B<\/p>\n<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h4 data-start=\"442\" data-end=\"485\">\ud83d\udd22 <strong data-start=\"450\" data-end=\"485\">Venn Diagram Trick (Shortcuts):<\/strong><\/h4>\n<p data-start=\"487\" data-end=\"648\">\ud83d\udccc <strong data-start=\"490\" data-end=\"502\">Problem:<\/strong> In a class of 100 students, 60 like math, 45 like physics, and 20 like both. Find how many like <strong data-start=\"599\" data-end=\"612\">only math<\/strong>, <strong data-start=\"614\" data-end=\"630\">only physics<\/strong>, and <strong data-start=\"636\" data-end=\"647\">neither<\/strong>.<\/p>\n<p data-start=\"650\" data-end=\"775\"><strong data-start=\"650\" data-end=\"668\">Trick Formula:<\/strong><br data-start=\"668\" data-end=\"671\" \/>\u2192 <strong data-start=\"673\" data-end=\"697\">Only A = A \u2212 (A \u2229 B)<\/strong><br data-start=\"697\" data-end=\"700\" \/>\u2192 <strong data-start=\"702\" data-end=\"726\">Only B = B \u2212 (A \u2229 B)<\/strong><br data-start=\"726\" data-end=\"729\" \/>\u2192 <strong data-start=\"731\" data-end=\"775\">Total = Only A + Only B + Both + Neither<\/strong><\/p>\n<p data-start=\"777\" data-end=\"792\"><strong data-start=\"777\" data-end=\"790\">Solution:<\/strong><\/p>\n<ul data-start=\"793\" data-end=\"933\">\n<li data-start=\"793\" data-end=\"821\">\n<p data-start=\"795\" data-end=\"821\">Only Math = 60 \u2212 20 = 40<\/p>\n<\/li>\n<li data-start=\"822\" data-end=\"853\">\n<p data-start=\"824\" data-end=\"853\">Only Physics = 45 \u2212 20 = 25<\/p>\n<\/li>\n<li data-start=\"854\" data-end=\"905\">\n<p data-start=\"856\" data-end=\"905\">Total liking either or both = 40 + 25 + 20 = 85<\/p>\n<\/li>\n<li data-start=\"906\" data-end=\"933\">\n<p data-start=\"908\" data-end=\"933\">Neither = 100 \u2212 85 = 15 \u2705<\/p>\n<\/li>\n<\/ul>\n<hr data-start=\"935\" data-end=\"938\" \/>\n<h3 data-start=\"940\" data-end=\"998\">\ud83d\udd39 <strong data-start=\"947\" data-end=\"998\">\ud83d\udccd Part B: Maxima &amp; Minima (Short Trick Method)<\/strong><\/h3>\n<h4 data-start=\"1000\" data-end=\"1020\">\u2705 What to Know:<\/h4>\n<ul data-start=\"1021\" data-end=\"1164\">\n<li data-start=\"1021\" data-end=\"1164\">\n<p data-start=\"1023\" data-end=\"1094\">Maxima\/Minima come from <strong data-start=\"1047\" data-end=\"1066\">differentiation<\/strong>:<br data-start=\"1067\" data-end=\"1070\" \/>If <code data-start=\"1075\" data-end=\"1086\">f\u2032(x) = 0<\/code>, and:<\/p>\n<ul data-start=\"1097\" data-end=\"1164\">\n<li data-start=\"1097\" data-end=\"1129\">\n<p data-start=\"1099\" data-end=\"1129\"><code data-start=\"1099\" data-end=\"1111\">f\u2032\u2032(x) &gt; 0<\/code> \u21d2 local minimum<\/p>\n<\/li>\n<li data-start=\"1132\" data-end=\"1164\">\n<p data-start=\"1134\" data-end=\"1164\"><code data-start=\"1134\" data-end=\"1146\">f\u2032\u2032(x) &lt; 0<\/code> \u21d2 local maximum<\/p>\n<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<hr data-start=\"1166\" data-end=\"1169\" \/>\n<h4 data-start=\"1171\" data-end=\"1203\">\ud83d\udd22 <strong data-start=\"1179\" data-end=\"1203\">Short Trick Example:<\/strong><\/h4>\n<p data-start=\"1205\" data-end=\"1285\">\ud83d\udccc <strong data-start=\"1208\" data-end=\"1220\">Problem:<\/strong> What is the maximum value of the function <code data-start=\"1263\" data-end=\"1284\">f(x) = \u2212x\u00b2 + 4x + 1<\/code>?<\/p>\n<p data-start=\"1287\" data-end=\"1306\"><strong data-start=\"1287\" data-end=\"1306\">Shortcut Steps:<\/strong><\/p>\n<ol data-start=\"1307\" data-end=\"1509\">\n<li data-start=\"1307\" data-end=\"1353\">\n<p data-start=\"1310\" data-end=\"1353\">It\u2019s a <strong data-start=\"1317\" data-end=\"1330\">quadratic<\/strong> of form <code data-start=\"1339\" data-end=\"1353\">ax\u00b2 + bx + c<\/code><\/p>\n<\/li>\n<li data-start=\"1354\" data-end=\"1416\">\n<p data-start=\"1357\" data-end=\"1416\">If <strong data-start=\"1360\" data-end=\"1369\">a &lt; 0<\/strong>, parabola opens downward \u21d2 <strong data-start=\"1397\" data-end=\"1404\">max<\/strong> at vertex<\/p>\n<\/li>\n<li data-start=\"1417\" data-end=\"1462\">\n<p data-start=\"1420\" data-end=\"1462\">Max value at <code data-start=\"1433\" data-end=\"1460\">x = \u2212b\/2a = \u22124\/(2\u00d7\u22121) = 2<\/code><\/p>\n<\/li>\n<li data-start=\"1463\" data-end=\"1509\">\n<p data-start=\"1466\" data-end=\"1509\"><code data-start=\"1466\" data-end=\"1507\">f(2) = \u2212(2)\u00b2 + 4\u00d72 + 1 = \u22124 + 8 + 1 = 5<\/code> \u2705<\/p>\n<\/li>\n<\/ol>\n<p data-start=\"1511\" data-end=\"1543\">So, <strong data-start=\"1515\" data-end=\"1530\">Maximum = 5<\/strong> at <strong data-start=\"1534\" data-end=\"1543\">x = 2<\/strong><\/p>\n<hr data-start=\"1545\" data-end=\"1548\" \/>\n<h3 data-start=\"1550\" data-end=\"1566\">\ud83d\udca1 GATE Tip:<\/h3>\n<ul data-start=\"1567\" data-end=\"1744\">\n<li data-start=\"1567\" data-end=\"1645\">\n<p data-start=\"1569\" data-end=\"1645\">For most <strong data-start=\"1578\" data-end=\"1592\">Set Theory<\/strong> problems, Venn diagram + formula trick works best.<\/p>\n<\/li>\n<li data-start=\"1646\" data-end=\"1744\">\n<p data-start=\"1648\" data-end=\"1744\">For <strong data-start=\"1652\" data-end=\"1669\">Maxima\/Minima<\/strong> in aptitude, always check if it\u2019s a quadratic \u2192 use vertex formula <code data-start=\"1737\" data-end=\"1744\">\u2212b\/2a<\/code><\/p>\n<\/li>\n<\/ul>\n<hr data-start=\"1746\" data-end=\"1749\" \/>\n<h3 data-start=\"1751\" data-end=\"1768\">\ud83c\udf81 Want More?<\/h3>\n<p data-start=\"1770\" data-end=\"1785\">Would you like:<\/p>\n<ul data-start=\"1786\" data-end=\"1971\">\n<li data-start=\"1786\" data-end=\"1835\">\n<p data-start=\"1788\" data-end=\"1835\">\ud83d\udcc4 PDF notes with 5+ solved tricks per topic?<\/p>\n<\/li>\n<li data-start=\"1836\" data-end=\"1903\">\n<p data-start=\"1838\" data-end=\"1903\">\ud83c\udfa5 Lecture slides with animation for GATE-style Venn questions?<\/p>\n<\/li>\n<li data-start=\"1904\" data-end=\"1971\">\n<p data-start=\"1906\" data-end=\"1971\">\ud83d\udcdd GATE PYQs (Previous Year Questions) from Set Theory &amp; Max-Min?<\/p>\n<\/li>\n<\/ul>\n<p data-start=\"1973\" data-end=\"2070\" data-is-last-node=\"\" data-is-only-node=\"\">Let me know, and I\u2019ll prepare a Part 2 with <strong data-start=\"2017\" data-end=\"2056\">word problems + optimization tricks<\/strong> for aptitude!<\/p>\n<h3 data-start=\"1973\" data-end=\"2070\"><a href=\"https:\/\/blogmedia.testbook.com\/blog\/wp-content\/uploads\/2018\/01\/maxima-and-minima-gate-study-material-in-pdf-0f9b7b0a.pdf\" target=\"_blank\" rel=\"noopener\">General Aptitude For Gate CSEIT &#8211; Set Theory Maxima-Minima Using Short Trick Method Part 1.<\/a><\/h3>\n<h3 class=\"LC20lb MBeuO DKV0Md\"><a href=\"https:\/\/www.jaipuria.ac.in\/blog\/wp-content\/uploads\/2023\/07\/Quant-Short-Tricks-PDF.pdf\" target=\"_blank\" rel=\"noopener\">QUALITATIVE APTITUDE TRICKS &amp; SHORTCUTS FOR<\/a><\/h3>\n<h3 class=\"LC20lb MBeuO DKV0Md\"><a href=\"https:\/\/gnindia.dronacharya.info\/Study-Materials\/Download\/General-GATE-Aptitude-Book.pdf\" target=\"_blank\" rel=\"noopener\">General-GATE-Aptitude-Book.pdf<\/a><\/h3>\n<h3 class=\"LC20lb MBeuO DKV0Md\"><a href=\"https:\/\/www.mathcentre.ac.uk\/resources\/uploaded\/mc-ty-maxmin-2009-1.pdf\" target=\"_blank\" rel=\"noopener\">Maxima and minima<\/a><\/h3>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/article>\n","protected":false},"excerpt":{"rendered":"<p>General Aptitude For Gate CSEIT &#8211; Set Theory Maxima-Minima Using Short Trick Method Part 1. [fvplayer id=&#8221;391&#8243;] \u00a0Set Theory \u2013 Maxima &amp; Minima Short Tricks for GATE CSE\/IT Set Theory is an important topic in GATE Computer Science &amp; IT. Questions related to Maxima and Minima of sets often appear in Aptitude &amp; Discrete Mathematics. [&hellip;]<\/p>\n","protected":false},"author":66,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[13],"tags":[],"class_list":["post-3406","post","type-post","status-publish","format-standard","hentry","category-general-aptitude"],"_links":{"self":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts\/3406","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\/66"}],"replies":[{"embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/comments?post=3406"}],"version-history":[{"count":0,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts\/3406\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/media?parent=3406"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/categories?post=3406"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/tags?post=3406"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}