{"id":2950,"date":"2025-06-07T07:15:35","date_gmt":"2025-06-07T07:15:35","guid":{"rendered":"https:\/\/diznr.com\/?p=2950"},"modified":"2025-06-07T07:15:35","modified_gmt":"2025-06-07T07:15:35","slug":"short-trick-method-for-solving-propositions-argument-based-problem-of-discrete-mathematics-2021-gate","status":"publish","type":"post","link":"https:\/\/www.reilsolar.com\/pdf\/short-trick-method-for-solving-propositions-argument-based-problem-of-discrete-mathematics-2021-gate\/","title":{"rendered":"Short trick method for solving propositions argument based problem of discrete mathematics-GATE 2025."},"content":{"rendered":"<p>Short trick method for solving propositions argument based problem of discrete mathematics-GATE 2025.<\/p>\n<p>[fvplayer id=&#8221;185&#8243;]<\/p>\n<p class=\"\" data-start=\"0\" data-end=\"164\">Here&#8217;s a <strong data-start=\"9\" data-end=\"31\">short-trick method<\/strong> for solving <strong data-start=\"44\" data-end=\"84\">Propositions\/Argument-Based Problems<\/strong> in <strong data-start=\"88\" data-end=\"112\">Discrete Mathematics<\/strong> \u2013 highly useful for <strong data-start=\"133\" data-end=\"153\">GATE 2025 CSE\/IT<\/strong> aspirants.<\/p>\n<hr class=\"\" data-start=\"166\" data-end=\"169\" \/>\n<h2 class=\"\" data-start=\"171\" data-end=\"245\">\ud83e\udde0 <strong data-start=\"177\" data-end=\"245\">Topic: Propositional Logic (Argument Validity) \u2013 Shortcut Method<\/strong><\/h2>\n<h3 class=\"\" data-start=\"247\" data-end=\"271\">\ud83c\udfaf What is the Goal?<\/h3>\n<p class=\"\" data-start=\"273\" data-end=\"293\">You are often asked:<\/p>\n<blockquote data-start=\"294\" data-end=\"398\">\n<p class=\"\" data-start=\"296\" data-end=\"398\"><em data-start=\"296\" data-end=\"323\">\u201cIs this argument valid?\u201d<\/em><br data-start=\"323\" data-end=\"326\" \/>Or<br data-start=\"330\" data-end=\"333\" \/><em data-start=\"335\" data-end=\"398\">\u201cWhich conclusion logically follows from the given premises?\u201d<\/em><\/p>\n<\/blockquote>\n<p class=\"\" data-start=\"400\" data-end=\"487\">Instead of using truth tables (which are time-consuming), use this <strong data-start=\"467\" data-end=\"486\">shortcut method<\/strong>:<\/p>\n<hr class=\"\" data-start=\"489\" data-end=\"492\" \/>\n<h2 class=\"\" data-start=\"494\" data-end=\"571\">\ud83d\udd0d <strong data-start=\"500\" data-end=\"571\">TRICK: Use the \u201cAssume True Premises, Test False Conclusion\u201d Method<\/strong><\/h2>\n<h3 class=\"\" data-start=\"573\" data-end=\"592\">\u2705 Step-by-Step:<\/h3>\n<ol data-start=\"594\" data-end=\"843\">\n<li class=\"\" data-start=\"594\" data-end=\"629\">\n<p class=\"\" data-start=\"597\" data-end=\"629\"><strong data-start=\"597\" data-end=\"629\">Assume all premises are TRUE<\/strong><\/p>\n<\/li>\n<li class=\"\" data-start=\"630\" data-end=\"667\">\n<p class=\"\" data-start=\"633\" data-end=\"667\"><strong data-start=\"633\" data-end=\"667\">Assume the conclusion is FALSE<\/strong><\/p>\n<\/li>\n<li class=\"\" data-start=\"668\" data-end=\"843\">\n<p class=\"\" data-start=\"671\" data-end=\"750\"><strong data-start=\"671\" data-end=\"729\">Try to find a truth assignment (T\/F for each variable)<\/strong> that satisfies both.<\/p>\n<ul data-start=\"754\" data-end=\"843\">\n<li class=\"\" data-start=\"754\" data-end=\"796\">\n<p class=\"\" data-start=\"756\" data-end=\"796\">If you <strong data-start=\"763\" data-end=\"770\">can<\/strong>, argument is <strong data-start=\"784\" data-end=\"795\">invalid<\/strong>.<\/p>\n<\/li>\n<li class=\"\" data-start=\"800\" data-end=\"843\">\n<p class=\"\" data-start=\"802\" data-end=\"843\">If you <strong data-start=\"809\" data-end=\"819\">cannot<\/strong>, argument is <strong data-start=\"833\" data-end=\"842\">valid<\/strong>.<\/p>\n<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n<hr class=\"\" data-start=\"845\" data-end=\"848\" \/>\n<h3 class=\"\" data-start=\"850\" data-end=\"887\">\ud83d\udcd8 Example Question (GATE Style):<\/h3>\n<p class=\"\" data-start=\"889\" data-end=\"895\">Given:<\/p>\n<ul data-start=\"896\" data-end=\"963\">\n<li class=\"\" data-start=\"896\" data-end=\"918\">\n<p class=\"\" data-start=\"898\" data-end=\"918\">Premise 1:\u202f<em data-start=\"909\" data-end=\"916\">p \u2192 q<\/em><\/p>\n<\/li>\n<li class=\"\" data-start=\"919\" data-end=\"941\">\n<p class=\"\" data-start=\"921\" data-end=\"941\">Premise 2:\u202f<em data-start=\"932\" data-end=\"939\">q \u2192 r<\/em><\/p>\n<\/li>\n<li class=\"\" data-start=\"942\" data-end=\"963\">\n<p class=\"\" data-start=\"944\" data-end=\"963\">Conclusion:\u202f<em data-start=\"956\" data-end=\"963\">p \u2192 r<\/em><\/p>\n<\/li>\n<\/ul>\n<p class=\"\" data-start=\"965\" data-end=\"987\">Is the argument valid?<\/p>\n<hr class=\"\" data-start=\"989\" data-end=\"992\" \/>\n<h3 class=\"\" data-start=\"994\" data-end=\"1017\">\ud83d\udd0d Apply the Trick:<\/h3>\n<ol data-start=\"1019\" data-end=\"1168\">\n<li class=\"\" data-start=\"1019\" data-end=\"1093\">\n<p class=\"\" data-start=\"1022\" data-end=\"1051\">Assume premises are <strong data-start=\"1042\" data-end=\"1050\">true<\/strong>:<\/p>\n<ul data-start=\"1055\" data-end=\"1093\">\n<li class=\"\" data-start=\"1055\" data-end=\"1072\">\n<p class=\"\" data-start=\"1057\" data-end=\"1072\"><em data-start=\"1057\" data-end=\"1064\">p \u2192 q<\/em> is true<\/p>\n<\/li>\n<li class=\"\" data-start=\"1076\" data-end=\"1093\">\n<p class=\"\" data-start=\"1078\" data-end=\"1093\"><em data-start=\"1078\" data-end=\"1085\">q \u2192 r<\/em> is true<\/p>\n<\/li>\n<\/ul>\n<\/li>\n<li class=\"\" data-start=\"1095\" data-end=\"1168\">\n<p class=\"\" data-start=\"1098\" data-end=\"1129\">Assume conclusion is <strong data-start=\"1119\" data-end=\"1128\">false<\/strong>:<\/p>\n<ul data-start=\"1133\" data-end=\"1168\">\n<li class=\"\" data-start=\"1133\" data-end=\"1168\">\n<p class=\"\" data-start=\"1135\" data-end=\"1168\"><em data-start=\"1135\" data-end=\"1142\">p \u2192 r<\/em> is false \u27f9 <em data-start=\"1154\" data-end=\"1168\">p = T, r = F<\/em><\/p>\n<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n<p class=\"\" data-start=\"1170\" data-end=\"1180\">Now check:<\/p>\n<ul data-start=\"1181\" data-end=\"1329\">\n<li class=\"\" data-start=\"1181\" data-end=\"1190\">\n<p class=\"\" data-start=\"1183\" data-end=\"1190\"><em data-start=\"1183\" data-end=\"1190\">p = T<\/em><\/p>\n<\/li>\n<li class=\"\" data-start=\"1191\" data-end=\"1200\">\n<p class=\"\" data-start=\"1193\" data-end=\"1200\"><em data-start=\"1193\" data-end=\"1200\">r = F<\/em><\/p>\n<\/li>\n<li class=\"\" data-start=\"1201\" data-end=\"1251\">\n<p class=\"\" data-start=\"1203\" data-end=\"1251\">For <em data-start=\"1207\" data-end=\"1214\">p \u2192 q<\/em> to be true and <em data-start=\"1230\" data-end=\"1237\">p = T<\/em>, then <em data-start=\"1244\" data-end=\"1251\">q = T<\/em><\/p>\n<\/li>\n<li class=\"\" data-start=\"1252\" data-end=\"1329\">\n<p class=\"\" data-start=\"1254\" data-end=\"1329\">For <em data-start=\"1258\" data-end=\"1265\">q \u2192 r<\/em> to be true and <em data-start=\"1281\" data-end=\"1288\">q = T<\/em>, then <em data-start=\"1295\" data-end=\"1302\">r = T<\/em> \u274c (but we assumed <em data-start=\"1321\" data-end=\"1328\">r = F<\/em>)<\/p>\n<\/li>\n<\/ul>\n<p class=\"\" data-start=\"1331\" data-end=\"1377\">\u274c Contradiction. So no such assignment exists.<\/p>\n<p class=\"\" data-start=\"1379\" data-end=\"1414\">\u2705 <strong data-start=\"1381\" data-end=\"1414\">Conclusion: Argument is Valid<\/strong><\/p>\n<hr class=\"\" data-start=\"1416\" data-end=\"1419\" \/>\n<h2 class=\"\" data-start=\"1421\" data-end=\"1464\">\u26a1 <strong data-start=\"1426\" data-end=\"1464\">Bonus Shortcut Symbols to Remember<\/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=\"1466\" data-end=\"1701\">\n<thead data-start=\"1466\" data-end=\"1498\">\n<tr data-start=\"1466\" data-end=\"1498\">\n<th data-start=\"1466\" data-end=\"1475\" data-col-size=\"sm\">Symbol<\/th>\n<th data-start=\"1475\" data-end=\"1498\" data-col-size=\"sm\">Meaning<\/th>\n<\/tr>\n<\/thead>\n<tbody data-start=\"1533\" data-end=\"1701\">\n<tr data-start=\"1533\" data-end=\"1566\">\n<td data-start=\"1533\" data-end=\"1542\" data-col-size=\"sm\">\u2227<\/td>\n<td data-col-size=\"sm\" data-start=\"1542\" data-end=\"1566\">AND<\/td>\n<\/tr>\n<tr data-start=\"1567\" data-end=\"1600\">\n<td data-start=\"1567\" data-end=\"1576\" data-col-size=\"sm\">\u2228<\/td>\n<td data-col-size=\"sm\" data-start=\"1576\" data-end=\"1600\">OR<\/td>\n<\/tr>\n<tr data-start=\"1601\" data-end=\"1634\">\n<td data-start=\"1601\" data-end=\"1610\" data-col-size=\"sm\">\u2192<\/td>\n<td data-start=\"1610\" data-end=\"1634\" data-col-size=\"sm\">IMPLIES<\/td>\n<\/tr>\n<tr data-start=\"1635\" data-end=\"1667\">\n<td data-start=\"1635\" data-end=\"1644\" data-col-size=\"sm\">\u2194<\/td>\n<td data-start=\"1644\" data-end=\"1667\" data-col-size=\"sm\">BICONDITIONAL (IFF)<\/td>\n<\/tr>\n<tr data-start=\"1668\" data-end=\"1701\">\n<td data-start=\"1668\" data-end=\"1677\" data-col-size=\"sm\">\u00ac<\/td>\n<td data-col-size=\"sm\" data-start=\"1677\" data-end=\"1701\">NOT (Negation)<\/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 class=\"\" data-start=\"1703\" data-end=\"1706\" \/>\n<h2 class=\"\" data-start=\"1708\" data-end=\"1756\">\u2728 Truth Value Hints (for implication <code data-start=\"1748\" data-end=\"1755\">p \u2192 q<\/code>)<\/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=\"1758\" data-end=\"1871\">\n<thead data-start=\"1758\" data-end=\"1775\">\n<tr data-start=\"1758\" data-end=\"1775\">\n<th data-start=\"1758\" data-end=\"1762\" data-col-size=\"sm\">p<\/th>\n<th data-start=\"1762\" data-end=\"1766\" data-col-size=\"sm\">q<\/th>\n<th data-start=\"1766\" data-end=\"1775\" data-col-size=\"sm\">p \u2192 q<\/th>\n<\/tr>\n<\/thead>\n<tbody data-start=\"1795\" data-end=\"1871\">\n<tr data-start=\"1795\" data-end=\"1813\">\n<td data-start=\"1795\" data-end=\"1799\" data-col-size=\"sm\">T<\/td>\n<td data-col-size=\"sm\" data-start=\"1799\" data-end=\"1803\">T<\/td>\n<td data-col-size=\"sm\" data-start=\"1803\" data-end=\"1813\">T<\/td>\n<\/tr>\n<tr data-start=\"1814\" data-end=\"1833\">\n<td data-start=\"1814\" data-end=\"1818\" data-col-size=\"sm\">T<\/td>\n<td data-start=\"1818\" data-end=\"1822\" data-col-size=\"sm\">F<\/td>\n<td data-col-size=\"sm\" data-start=\"1822\" data-end=\"1833\"><strong data-start=\"1826\" data-end=\"1831\">F<\/strong><\/td>\n<\/tr>\n<tr data-start=\"1834\" data-end=\"1852\">\n<td data-start=\"1834\" data-end=\"1838\" data-col-size=\"sm\">F<\/td>\n<td data-col-size=\"sm\" data-start=\"1838\" data-end=\"1842\">T<\/td>\n<td data-col-size=\"sm\" data-start=\"1842\" data-end=\"1852\">T<\/td>\n<\/tr>\n<tr data-start=\"1853\" data-end=\"1871\">\n<td data-start=\"1853\" data-end=\"1857\" data-col-size=\"sm\">F<\/td>\n<td data-start=\"1857\" data-end=\"1861\" data-col-size=\"sm\">F<\/td>\n<td data-col-size=\"sm\" data-start=\"1861\" data-end=\"1871\">T<\/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<p class=\"\" data-start=\"1873\" data-end=\"1908\"><strong data-start=\"1873\" data-end=\"1908\">Only false when p = T and q = F<\/strong><\/p>\n<hr class=\"\" data-start=\"1910\" data-end=\"1913\" \/>\n<h2 class=\"\" data-start=\"1915\" data-end=\"1931\">\ud83d\udccc Fast Tips:<\/h2>\n<ul data-start=\"1933\" data-end=\"2121\">\n<li class=\"\" data-start=\"1933\" data-end=\"1995\">\n<p class=\"\" data-start=\"1935\" data-end=\"1995\"><strong data-start=\"1935\" data-end=\"1958\">Conjunction (p \u2227 q)<\/strong> is <strong data-start=\"1962\" data-end=\"1971\">false<\/strong> if <strong data-start=\"1975\" data-end=\"1995\">any one is false<\/strong><\/p>\n<\/li>\n<li class=\"\" data-start=\"1996\" data-end=\"2056\">\n<p class=\"\" data-start=\"1998\" data-end=\"2056\"><strong data-start=\"1998\" data-end=\"2021\">Disjunction (p \u2228 q)<\/strong> is <strong data-start=\"2025\" data-end=\"2033\">true<\/strong> if <strong data-start=\"2037\" data-end=\"2056\">any one is true<\/strong><\/p>\n<\/li>\n<li class=\"\" data-start=\"2057\" data-end=\"2121\">\n<p class=\"\" data-start=\"2059\" data-end=\"2121\"><strong data-start=\"2059\" data-end=\"2082\">Implication (p \u2192 q)<\/strong> is only <strong data-start=\"2091\" data-end=\"2121\">false when p = T and q = F<\/strong><\/p>\n<\/li>\n<\/ul>\n<hr class=\"\" data-start=\"2123\" data-end=\"2126\" \/>\n<h2 class=\"\" data-start=\"2128\" data-end=\"2146\">\ud83e\uddea Practice It:<\/h2>\n<p class=\"\" data-start=\"2148\" data-end=\"2160\">\ud83d\udc49 Try this:<\/p>\n<p class=\"\" data-start=\"2162\" data-end=\"2171\">Premises:<\/p>\n<ol data-start=\"2172\" data-end=\"2197\">\n<li class=\"\" data-start=\"2172\" data-end=\"2185\">\n<p class=\"\" data-start=\"2175\" data-end=\"2185\"><em data-start=\"2175\" data-end=\"2183\">\u00acp \u2228 q<\/em><\/p>\n<\/li>\n<li class=\"\" data-start=\"2186\" data-end=\"2197\">\n<p class=\"\" data-start=\"2189\" data-end=\"2197\"><em data-start=\"2189\" data-end=\"2197\">\u00acq \u2228 r<\/em><\/p>\n<\/li>\n<\/ol>\n<p class=\"\" data-start=\"2199\" data-end=\"2219\">Conclusion:<br \/>\n<em data-start=\"2211\" data-end=\"2219\">\u00acp \u2228 r<\/em><\/p>\n<p class=\"\" data-start=\"2221\" data-end=\"2301\">Try using the same trick and you&#8217;ll quickly conclude: the argument is <strong data-start=\"2291\" data-end=\"2300\">valid<\/strong>.<\/p>\n<hr class=\"\" data-start=\"2303\" data-end=\"2306\" \/>\n<p class=\"\" data-start=\"2308\" data-end=\"2427\">Would you like a <strong data-start=\"2325\" data-end=\"2346\">PDF notes version<\/strong>, <strong data-start=\"2348\" data-end=\"2369\">practice problems<\/strong>, or a <strong data-start=\"2376\" data-end=\"2411\">video explanation with examples<\/strong> for this topic?<\/p>\n<h3 data-start=\"2308\" data-end=\"2427\"><a href=\"https:\/\/www2.cs.uh.edu\/~arjun\/courses\/ds\/DiscMaths4CompSc.pdf\" target=\"_blank\" rel=\"noopener\">Short trick method for solving propositions argument based problem of discrete mathematics-GATE 2025.<\/a><\/h3>\n<h3 class=\"LC20lb MBeuO DKV0Md\"><a href=\"https:\/\/www.cs.yale.edu\/homes\/aspnes\/classes\/202\/notes.pdf\" target=\"_blank\" rel=\"noopener\">Notes on Discrete Mathematics<\/a><\/h3>\n<h3 class=\"LC20lb MBeuO DKV0Md\"><a href=\"https:\/\/mrce.in\/ebooks\/Maths-Discrete%20Mathematics%20&amp;%20its%20Applications%208th%20Ed.pdf\" target=\"_blank\" rel=\"noopener\">Discrete Mathematics and Its Applications, Eighth Edition<\/a><\/h3>\n","protected":false},"excerpt":{"rendered":"<p>Short trick method for solving propositions argument based problem of discrete mathematics-GATE 2025. [fvplayer id=&#8221;185&#8243;] Here&#8217;s a short-trick method for solving Propositions\/Argument-Based Problems in Discrete Mathematics \u2013 highly useful for GATE 2025 CSE\/IT aspirants. \ud83e\udde0 Topic: Propositional Logic (Argument Validity) \u2013 Shortcut Method \ud83c\udfaf What is the Goal? You are often asked: \u201cIs this argument [&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-2950","post","type-post","status-publish","format-standard","hentry","category-discrete-mathematics"],"_links":{"self":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts\/2950","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=2950"}],"version-history":[{"count":0,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts\/2950\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/media?parent=2950"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/categories?post=2950"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/tags?post=2950"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}