{"id":2978,"date":"2025-06-06T13:27:04","date_gmt":"2025-06-06T13:27:04","guid":{"rendered":"https:\/\/diznr.com\/?p=2978"},"modified":"2025-06-06T13:27:04","modified_gmt":"2025-06-06T13:27:04","slug":"day-04part-14-discrete-mathematics-for-computer-science-example-based-on-implication-02-part","status":"publish","type":"post","link":"https:\/\/www.reilsolar.com\/pdf\/day-04part-14-discrete-mathematics-for-computer-science-example-based-on-implication-02-part\/","title":{"rendered":"Day 04Part 14- Discrete mathematics for computer science &#8211; Example based on implication part 02"},"content":{"rendered":"<p>Day 04Part 14- Discrete mathematics for computer science &#8211; Example based on implication part 02<\/p>\n<p>[fvplayer id=&#8221;197&#8243;]<\/p>\n<p data-start=\"0\" data-end=\"242\">Implication, often expressed as &#8220;if <span class=\"katex\"><span class=\"katex-mathml\">pp<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">p<\/span><\/span><\/span><\/span>, then <span class=\"katex\"><span class=\"katex-mathml\">qq<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">q<\/span><\/span><\/span><\/span>&#8221; (denoted <span class=\"katex\"><span class=\"katex-mathml\">p\u2192qp \\rightarrow q<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">p<\/span><span class=\"mrel\">\u2192<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">q<\/span><\/span><\/span><\/span>), is a fundamental concept in discrete mathematics and computer science. Understanding its nuances is crucial for logical reasoning and problem-solving.<\/p>\n<p data-start=\"244\" data-end=\"276\"><strong data-start=\"244\" data-end=\"276\">Truth Table for Implication:<\/strong><\/p>\n<table data-start=\"278\" data-end=\"538\">\n<thead data-start=\"278\" data-end=\"323\">\n<tr data-start=\"278\" data-end=\"323\">\n<th data-start=\"278\" data-end=\"288\"><span class=\"katex\"><span class=\"katex-mathml\">pp<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">p<\/span><\/span><\/span><\/span><\/th>\n<th data-start=\"288\" data-end=\"298\"><span class=\"katex\"><span class=\"katex-mathml\">qq<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">q<\/span><\/span><\/span><\/span><\/th>\n<th data-start=\"298\" data-end=\"323\"><span class=\"katex\"><span class=\"katex-mathml\">p\u2192qp \\rightarrow q<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">p<\/span><span class=\"mrel\">\u2192<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">q<\/span><\/span><\/span><\/span><\/th>\n<\/tr>\n<\/thead>\n<tbody data-start=\"367\" data-end=\"538\">\n<tr data-start=\"367\" data-end=\"409\">\n<td>T<\/td>\n<td>T<\/td>\n<td>T<\/td>\n<\/tr>\n<tr data-start=\"410\" data-end=\"452\">\n<td>T<\/td>\n<td>F<\/td>\n<td>F<\/td>\n<\/tr>\n<tr data-start=\"453\" data-end=\"495\">\n<td>F<\/td>\n<td>T<\/td>\n<td>T<\/td>\n<\/tr>\n<tr data-start=\"496\" data-end=\"538\">\n<td>F<\/td>\n<td>F<\/td>\n<td>T<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p data-start=\"540\" data-end=\"691\">This table indicates that an implication <span class=\"katex\"><span class=\"katex-mathml\">p\u2192qp \\rightarrow q<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">p<\/span><span class=\"mrel\">\u2192<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">q<\/span><\/span><\/span><\/span> is false only when <span class=\"katex\"><span class=\"katex-mathml\">pp<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">p<\/span><\/span><\/span><\/span> is true and <span class=\"katex\"><span class=\"katex-mathml\">qq<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">q<\/span><\/span><\/span><\/span> is false; in all other cases, it is true.<\/p>\n<p data-start=\"693\" data-end=\"707\"><strong data-start=\"693\" data-end=\"707\">Example 1:<\/strong><\/p>\n<ul data-start=\"709\" data-end=\"776\">\n<li data-start=\"709\" data-end=\"740\">Let <span class=\"katex\"><span class=\"katex-mathml\">pp<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">p<\/span><\/span><\/span><\/span>: &#8220;It is raining.&#8221;<\/li>\n<li data-start=\"741\" data-end=\"776\">Let <span class=\"katex\"><span class=\"katex-mathml\">qq<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">q<\/span><\/span><\/span><\/span>: &#8220;The ground is wet.&#8221;<\/li>\n<\/ul>\n<p data-start=\"778\" data-end=\"874\">The implication <span class=\"katex\"><span class=\"katex-mathml\">p\u2192qp \\rightarrow q<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">p<\/span><span class=\"mrel\">\u2192<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">q<\/span><\/span><\/span><\/span> translates to: &#8220;If it is raining, then the ground is wet.&#8221;<\/p>\n<ul data-start=\"876\" data-end=\"1237\">\n<li data-start=\"876\" data-end=\"983\">If it is raining ( <span class=\"katex\"><span class=\"katex-mathml\">pp<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">p<\/span><\/span><\/span><\/span> is true) and the ground is wet ( <span class=\"katex\"><span class=\"katex-mathml\">qq<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">q<\/span><\/span><\/span><\/span> is true), the implication holds true.<\/li>\n<li data-start=\"984\" data-end=\"1094\">If it is raining ( <span class=\"katex\"><span class=\"katex-mathml\">pp<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">p<\/span><\/span><\/span><\/span> is true) and the ground is not wet ( <span class=\"katex\"><span class=\"katex-mathml\">qq<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">q<\/span><\/span><\/span><\/span> is false), the implication is false.<\/li>\n<li data-start=\"1095\" data-end=\"1237\">If it is not raining ( <span class=\"katex\"><span class=\"katex-mathml\">pp<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">p<\/span><\/span><\/span><\/span> is false), regardless of the ground&#8217;s condition ( <span class=\"katex\"><span class=\"katex-mathml\">qq<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">q<\/span><\/span><\/span><\/span> true or false), the implication is considered true.<\/li>\n<\/ul>\n<p data-start=\"1239\" data-end=\"1253\"><strong data-start=\"1239\" data-end=\"1253\">Example 2:<\/strong><\/p>\n<ul data-start=\"1255\" data-end=\"1320\">\n<li data-start=\"1255\" data-end=\"1283\"><span class=\"katex\"><span class=\"katex-mathml\">pp<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">p<\/span><\/span><\/span><\/span>: &#8220;You study hard.&#8221;<\/li>\n<li data-start=\"1284\" data-end=\"1320\"><span class=\"katex\"><span class=\"katex-mathml\">qq<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">q<\/span><\/span><\/span><\/span>: &#8220;You will pass the exam.&#8221;<\/li>\n<\/ul>\n<p data-start=\"1322\" data-end=\"1416\">The implication <span class=\"katex\"><span class=\"katex-mathml\">p\u2192qp \\rightarrow q<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">p<\/span><span class=\"mrel\">\u2192<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">q<\/span><\/span><\/span><\/span> means: &#8220;If you study hard, then you will pass the exam.&#8221;<\/p>\n<ul data-start=\"1418\" data-end=\"1741\">\n<li data-start=\"1418\" data-end=\"1519\">If you study hard ( <span class=\"katex\"><span class=\"katex-mathml\">pp<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">p<\/span><\/span><\/span><\/span> is true) and pass the exam ( <span class=\"katex\"><span class=\"katex-mathml\">qq<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">q<\/span><\/span><\/span><\/span> is true), the implication is true.<\/li>\n<li data-start=\"1520\" data-end=\"1630\">If you study hard ( <span class=\"katex\"><span class=\"katex-mathml\">pp<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">p<\/span><\/span><\/span><\/span> is true) and do not pass the exam ( <span class=\"katex\"><span class=\"katex-mathml\">qq<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">q<\/span><\/span><\/span><\/span> is false), the implication is false.<\/li>\n<li data-start=\"1631\" data-end=\"1741\">If you do not study hard ( <span class=\"katex\"><span class=\"katex-mathml\">pp<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">p<\/span><\/span><\/span><\/span> is false), the implication is true regardless of whether you pass or not.<\/li>\n<\/ul>\n<p data-start=\"1743\" data-end=\"1789\"><strong data-start=\"1743\" data-end=\"1789\">Understanding the Implication Truth Table:<\/strong><\/p>\n<p data-start=\"1791\" data-end=\"2165\">The truth table for implication might seem counterintuitive, especially when <span class=\"katex\"><span class=\"katex-mathml\">pp<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">p<\/span><\/span><\/span><\/span> is false. However, in logical terms, an implication <span class=\"katex\"><span class=\"katex-mathml\">p\u2192qp \\rightarrow q<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">p<\/span><span class=\"mrel\">\u2192<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">q<\/span><\/span><\/span><\/span> is only false when <span class=\"katex\"><span class=\"katex-mathml\">pp<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">p<\/span><\/span><\/span><\/span> is true, and <span class=\"katex\"><span class=\"katex-mathml\">qq<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">q<\/span><\/span><\/span><\/span> is false. In all other scenarios, it is true. This definition aligns with the principle that a false hypothesis cannot lead to a false conclusion in logical reasoning.<\/p>\n<p data-start=\"2167\" data-end=\"2236\">For a more in-depth understanding, you might find this video helpful:<\/p>\n<div class=\"not-prose mb-3 flex flex-col gap-4 text-base\">\n<h3><a href=\"https:\/\/www2.cs.uh.edu\/~arjun\/courses\/ds\/DiscMaths4CompSc.pdf\" target=\"_blank\" rel=\"noopener\">Day 04Part 14- Discrete mathematics for computer science &#8211; Example based on implication part 02<\/a><\/h3>\n<h3 class=\"LC20lb MBeuO DKV0Md\"><a href=\"https:\/\/courses.cs.duke.edu\/spring09\/cps102\/Lectures\/Book.pdf\" target=\"_blank\" rel=\"noopener\">DISCRETE MATHEMATICS FOR COMPUTER SCIENCE<\/a><\/h3>\n<h3 class=\"LC20lb MBeuO DKV0Md\"><a href=\"https:\/\/www.cl.cam.ac.uk\/teaching\/1314\/DiscMath\/DiscMathNotes.pdf\" target=\"_blank\" rel=\"noopener\">Discrete Mathematics For Computer Science<\/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:\/\/sriindu.ac.in\/wp-content\/uploads\/2023\/10\/R20CSE2201-DISCRETE-MATHEMATICS.pdf\" target=\"_blank\" rel=\"noopener\">DISCRETE MATHEMATICS<\/a><\/h3>\n<p>\u0921\u093f\u0938\u094d\u0915\u094d\u0930\u0940\u091f \u092e\u0948\u0925\u092e\u0947\u091f\u093f\u0915\u094d\u0938 \u092e\u0947\u0902 <strong>\u0907\u092e\u094d\u092a\u094d\u0932\u093f\u0915\u0947\u0936\u0928 (Implication)<\/strong> \u090f\u0915 \u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u0935\u093f\u0937\u092f \u0939\u0948, \u0935\u093f\u0936\u0947\u0937\u0915\u0930 GATE \u091c\u0948\u0938\u0940 \u092a\u0930\u0940\u0915\u094d\u0937\u093e\u0913\u0902 \u092e\u0947\u0902\u0964 \u092f\u0939\u093e\u0901 \u0939\u092e \u0907\u092e\u094d\u092a\u094d\u0932\u093f\u0915\u0947\u0936\u0928 \u092a\u0930 \u0906\u0927\u093e\u0930\u093f\u0924 \u090f\u0915 \u0909\u0926\u093e\u0939\u0930\u0923 \u092a\u094d\u0930\u0938\u094d\u0924\u0941\u0924 \u0915\u0930 \u0930\u0939\u0947 \u0939\u0948\u0902 \u091c\u094b \u0906\u092a\u0915\u0947 \u0938\u092e\u091d \u0915\u094b \u0914\u0930 \u0917\u0939\u0930\u093e \u0915\u0930\u0947\u0917\u093e\u0964<\/p>\n<hr \/>\n<h3>\ud83d\udd39 \u0909\u0926\u093e\u0939\u0930\u0923 2: \u0907\u092e\u094d\u092a\u094d\u0932\u093f\u0915\u0947\u0936\u0928 \u0915\u093e \u0935\u094d\u092f\u093e\u0935\u0939\u093e\u0930\u093f\u0915 \u0909\u092a\u092f\u094b\u0917<\/h3>\n<p><strong>\u0915\u0925\u0928:<\/strong><br \/>\n&#8220;\u092f\u0926\u093f \u0915\u094b\u0908 \u091b\u093e\u0924\u094d\u0930 \u0928\u093f\u092f\u092e\u093f\u0924 \u0930\u0942\u092a \u0938\u0947 \u092a\u0922\u093c\u093e\u0908 \u0915\u0930\u0924\u093e \u0939\u0948, \u0924\u094b \u0935\u0939 \u092a\u0930\u0940\u0915\u094d\u0937\u093e \u092e\u0947\u0902 \u0909\u0924\u094d\u0924\u0940\u0930\u094d\u0923 \u0939\u094b\u0917\u093e\u0964&#8221;<\/p>\n<p><strong>\u092a\u094d\u0930\u092a\u094b\u091c\u093c\u093f\u0936\u0928\u0932 \u0930\u0942\u092a \u092e\u0947\u0902:<\/strong><\/p>\n<ul>\n<li><strong>P<\/strong>: \u091b\u093e\u0924\u094d\u0930 \u0928\u093f\u092f\u092e\u093f\u0924 \u0930\u0942\u092a \u0938\u0947 \u092a\u0922\u093c\u093e\u0908 \u0915\u0930\u0924\u093e \u0939\u0948\u0964<\/li>\n<li><strong>Q<\/strong>: \u091b\u093e\u0924\u094d\u0930 \u092a\u0930\u0940\u0915\u094d\u0937\u093e \u092e\u0947\u0902 \u0909\u0924\u094d\u0924\u0940\u0930\u094d\u0923 \u0939\u094b\u0924\u093e \u0939\u0948\u0964<\/li>\n<\/ul>\n<p><strong>\u0907\u092e\u094d\u092a\u094d\u0932\u093f\u0915\u0947\u0936\u0928:<\/strong> P \u2192 Q(Faculty KSU)<\/p>\n<p><strong>\u091f\u094d\u0930\u0941\u0925 \u091f\u0947\u092c\u0932:<\/strong><\/p>\n<table>\n<thead>\n<tr>\n<th>P (\u092a\u0922\u093c\u093e\u0908 \u0915\u0930\u0924\u093e \u0939\u0948)<\/th>\n<th>Q (\u0909\u0924\u094d\u0924\u0940\u0930\u094d\u0923 \u0939\u094b\u0924\u093e \u0939\u0948)<\/th>\n<th>P \u2192 Q (\u0907\u092e\u094d\u092a\u094d\u0932\u093f\u0915\u0947\u0936\u0928)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\u0938\u0924\u094d\u092f (T)<\/td>\n<td>\u0938\u0924\u094d\u092f (T)<\/td>\n<td>\u0938\u0924\u094d\u092f (T)<\/td>\n<\/tr>\n<tr>\n<td>\u0938\u0924\u094d\u092f (T)<\/td>\n<td>\u0905\u0938\u0924\u094d\u092f (F)<\/td>\n<td>\u0905\u0938\u0924\u094d\u092f (F)<\/td>\n<\/tr>\n<tr>\n<td>\u0905\u0938\u0924\u094d\u092f (F)<\/td>\n<td>\u0938\u0924\u094d\u092f (T)<\/td>\n<td>\u0938\u0924\u094d\u092f (T)<\/td>\n<\/tr>\n<tr>\n<td>\u0905\u0938\u0924\u094d\u092f (F)<\/td>\n<td>\u0905\u0938\u0924\u094d\u092f (F)<\/td>\n<td>\u0938\u0924\u094d\u092f (T)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><strong>\u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923:<\/strong><\/p>\n<ul>\n<li>\u092f\u0926\u093f \u091b\u093e\u0924\u094d\u0930 \u092a\u0922\u093c\u093e\u0908 \u0915\u0930\u0924\u093e \u0939\u0948 (P \u0938\u0924\u094d\u092f) \u0914\u0930 \u0909\u0924\u094d\u0924\u0940\u0930\u094d\u0923 \u0939\u094b\u0924\u093e \u0939\u0948 (Q \u0938\u0924\u094d\u092f), \u0924\u094b \u0907\u092e\u094d\u092a\u094d\u0932\u093f\u0915\u0947\u0936\u0928 \u0938\u0924\u094d\u092f \u0939\u0948\u0964<\/li>\n<li>\u092f\u0926\u093f \u091b\u093e\u0924\u094d\u0930 \u092a\u0922\u093c\u093e\u0908 \u0915\u0930\u0924\u093e \u0939\u0948 (P \u0938\u0924\u094d\u092f) \u0932\u0947\u0915\u093f\u0928 \u0909\u0924\u094d\u0924\u0940\u0930\u094d\u0923 \u0928\u0939\u0940\u0902 \u0939\u094b\u0924\u093e (Q \u0905\u0938\u0924\u094d\u092f), \u0924\u094b \u0907\u092e\u094d\u092a\u094d\u0932\u093f\u0915\u0947\u0936\u0928 \u0905\u0938\u0924\u094d\u092f \u0939\u0948\u0964<\/li>\n<li>\u092f\u0926\u093f \u091b\u093e\u0924\u094d\u0930 \u092a\u0922\u093c\u093e\u0908 \u0928\u0939\u0940\u0902 \u0915\u0930\u0924\u093e (P \u0905\u0938\u0924\u094d\u092f), \u0924\u094b \u091a\u093e\u0939\u0947 \u0935\u0939 \u0909\u0924\u094d\u0924\u0940\u0930\u094d\u0923 \u0939\u094b \u092f\u093e \u0928\u0939\u0940\u0902, \u0907\u092e\u094d\u092a\u094d\u0932\u093f\u0915\u0947\u0936\u0928 \u0938\u0924\u094d\u092f \u092e\u093e\u0928\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964<\/li>\n<\/ul>\n<hr \/>\n<h3>\ud83d\udd38 \u0907\u092e\u094d\u092a\u094d\u0932\u093f\u0915\u0947\u0936\u0928 \u0915\u0947 \u0905\u0928\u094d\u092f \u0930\u0942\u092a<\/h3>\n<ul>\n<li><strong>\u0915\u0928\u094d\u0935\u0930\u094d\u0938 (Converse):<\/strong> Q \u2192 P<\/li>\n<li><strong>\u0907\u0928\u0935\u0930\u094d\u0938 (Inverse):<\/strong> \u00acP \u2192 \u00acQ<\/li>\n<li><strong>\u0915\u0949\u0928\u094d\u091f\u094d\u0930\u093e\u092a\u0949\u091c\u093f\u091f\u093f\u0935 (Contrapositive):<\/strong> \u00acQ \u2192 \u00acP(YouTube)<\/li>\n<\/ul>\n<p>\u0907\u0928 \u0930\u0942\u092a\u094b\u0902 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0932\u0949\u091c\u093f\u0915\u0932 \u0924\u0930\u094d\u0915 \u0914\u0930 \u092a\u094d\u0930\u092e\u0947\u092f\u094b\u0902 \u0915\u0947 \u092a\u094d\u0930\u092e\u093e\u0923 \u092e\u0947\u0902 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964<\/p>\n<hr \/>\n<h3>\ud83d\udcda \u0905\u0924\u093f\u0930\u093f\u0915\u094d\u0924 \u0905\u0927\u094d\u092f\u092f\u0928 \u0938\u0902\u0938\u093e\u0927\u0928<\/h3>\n<ul>\n<li><strong>\u0935\u0940\u0921\u093f\u092f\u094b \u0935\u094d\u092f\u093e\u0916\u094d\u092f\u093e\u0928:<\/strong> \u0907\u092e\u094d\u092a\u094d\u0932\u093f\u0915\u0947\u0936\u0928 \u0914\u0930 \u0938\u0902\u092c\u0902\u0927\u093f\u0924 \u0905\u0935\u0927\u093e\u0930\u0923\u093e\u0913\u0902 \u092a\u0930 \u0935\u093f\u0938\u094d\u0924\u0943\u0924 \u091c\u093e\u0928\u0915\u093e\u0930\u0940 \u0915\u0947 \u0932\u093f\u090f \u092f\u0939 \u0935\u0940\u0921\u093f\u092f\u094b \u0926\u0947\u0916\u0947\u0902:Lecture 4: Implication, Conditional, Converse, Inverse, Contrapositive in Discrete Mathematics in Hindi<\/li>\n<li><strong>\u0932\u0947\u0916:<\/strong> \u092a\u094d\u0930\u092a\u094b\u091c\u093c\u093f\u0936\u0928\u0932 \u0932\u0949\u091c\u093f\u0915 \u0914\u0930 \u0907\u092e\u094d\u092a\u094d\u0932\u093f\u0915\u0947\u0936\u0928 \u092a\u0930 \u0935\u093f\u0938\u094d\u0924\u0943\u0924 \u0932\u0947\u0916 \u0915\u0947 \u0932\u093f\u090f GeeksforGeeks \u0915\u093e \u092f\u0939 \u092a\u0943\u0937\u094d\u0920 \u0926\u0947\u0916\u0947\u0902:Discrete Mathematics Tutorial &#8211; GeeksforGeeks<\/li>\n<\/ul>\n<hr \/>\n<p>\u092f\u0926\u093f \u0906\u092a \u0914\u0930 \u0905\u0927\u093f\u0915 \u0909\u0926\u093e\u0939\u0930\u0923, \u0905\u092d\u094d\u092f\u093e\u0938 \u092a\u094d\u0930\u0936\u094d\u0928 \u092f\u093e \u0915\u093f\u0938\u0940 \u0935\u093f\u0936\u0947\u0937 \u0905\u0935\u0927\u093e\u0930\u0923\u093e \u092a\u0930 \u0938\u094d\u092a\u0937\u094d\u091f\u0940\u0915\u0930\u0923 \u091a\u093e\u0939\u0924\u0947 \u0939\u0948\u0902, \u0924\u094b \u0915\u0943\u092a\u092f\u093e \u092c\u0924\u093e\u090f\u0902!<\/p>\n<h3><a href=\"https:\/\/unidel.edu.ng\/focelibrary\/books\/Discrete%20Mathematics%20for%20Computer%20Science%20(Pomde%20N.)%20(Z-Library).pdf\" target=\"_blank\" rel=\"noopener\">Day 04Part 14- Discrete mathematics for computer science &#8211; Example based on implication part 02<\/a><\/h3>\n<h3 class=\"LC20lb MBeuO DKV0Md\"><a href=\"https:\/\/faculty.ksu.edu.sa\/sites\/default\/files\/rosen_discrete_mathematics_and_its_applications_7th_edition.pdf\" target=\"_blank\" rel=\"noopener\">Discrete Mathematics and Its Applications, Seventh Edition<\/a><\/h3>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Day 04Part 14- Discrete mathematics for computer science &#8211; Example based on implication part 02 [fvplayer id=&#8221;197&#8243;] Implication, often expressed as &#8220;if ppp, then qqq&#8221; (denoted p\u2192qp \\rightarrow qp\u2192q), is a fundamental concept in discrete mathematics and computer science. Understanding its nuances is crucial for logical reasoning and problem-solving. Truth Table for Implication: ppp qqq [&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-2978","post","type-post","status-publish","format-standard","hentry","category-discrete-mathematics"],"_links":{"self":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts\/2978","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=2978"}],"version-history":[{"count":0,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts\/2978\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/media?parent=2978"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/categories?post=2978"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/tags?post=2978"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}