{"id":2988,"date":"2025-06-01T14:20:58","date_gmt":"2025-06-01T14:20:58","guid":{"rendered":"https:\/\/diznr.com\/?p=2988"},"modified":"2025-06-01T14:20:58","modified_gmt":"2025-06-01T14:20:58","slug":"day-04part-10-discrete-mathematics-for-gate-in-hindi-bi-conditional-or-if-and-only-if-statements","status":"publish","type":"post","link":"https:\/\/www.reilsolar.com\/pdf\/day-04part-10-discrete-mathematics-for-gate-in-hindi-bi-conditional-or-if-and-only-if-statements\/","title":{"rendered":"Day 04part 10- Discrete mathematics for gate in Hindi &#8211; Bi-conditional or if and only if statements."},"content":{"rendered":"<p>Day 04part 10- Discrete mathematics for gate in Hindi &#8211; Bi-conditional or if and only if statements.<\/p>\n<p>[fvplayer id=&#8221;203&#8243;]<\/p>\n<h3 data-start=\"0\" data-end=\"68\"><strong data-start=\"4\" data-end=\"66\">\u00a0Day 04 Part 10 &#8211; Discrete Mathematics for GATE in Hindi<\/strong><\/h3>\n<h3 data-start=\"69\" data-end=\"144\"><strong data-start=\"72\" data-end=\"142\">Bi-Conditional Statements (If and Only If &#8211; IFF) | \u0926\u094d\u0935\u093f-\u0936\u0930\u094d\u0924\u0940\u092f \u0915\u0925\u0928<\/strong><\/h3>\n<p data-start=\"146\" data-end=\"276\"><strong data-start=\"149\" data-end=\"162\">Language:<\/strong> Hindi<br data-start=\"168\" data-end=\"171\" \/><strong data-start=\"174\" data-end=\"184\">Topic:<\/strong> Bi-Conditional Statements<br data-start=\"210\" data-end=\"213\" \/><strong data-start=\"216\" data-end=\"225\">Part:<\/strong> 10<br data-start=\"228\" data-end=\"231\" \/><strong data-start=\"234\" data-end=\"249\">Exam Focus:<\/strong> GATE, UGC-NET, PSU Exams<\/p>\n<h3 data-start=\"283\" data-end=\"342\"><strong data-start=\"286\" data-end=\"340\">\u00a01. Bi-Conditional Statement (IFF) \u0915\u094d\u092f\u093e \u0939\u094b\u0924\u093e \u0939\u0948?<\/strong><\/h3>\n<p data-start=\"343\" data-end=\"501\"><strong data-start=\"345\" data-end=\"360\">Definition:<\/strong><br data-start=\"360\" data-end=\"363\" \/>Bi-Conditional Statement \u0915\u094b <strong data-start=\"391\" data-end=\"417\">&#8220;If and Only If (IFF)&#8221;<\/strong> \u0915\u0939\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964<br data-start=\"430\" data-end=\"433\" \/>\u0907\u0938\u0915\u093e \u092e\u0924\u0932\u092c \u0939\u0948 \u0915\u093f <strong data-start=\"449\" data-end=\"499\">\u0926\u094b\u0928\u094b\u0902 \u0938\u094d\u091f\u0947\u091f\u092e\u0947\u0902\u091f\u094d\u0938 \u090f\u0915-\u0926\u0942\u0938\u0930\u0947 \u092a\u0930 \u0928\u093f\u0930\u094d\u092d\u0930 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902\u0964<\/strong><\/p>\n<p data-start=\"503\" data-end=\"564\"><strong data-start=\"506\" data-end=\"517\">Symbol:<\/strong> <span class=\"katex\"><span class=\"katex-mathml\">p\u2005\u200a\u27fa\u2005\u200aqp \\iff q<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">p<\/span><span class=\"mrel\">\u27fa<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">q<\/span><\/span><\/span><\/span> (\u092a\u0922\u093c\u0947\u0902: &#8220;p if and only if q&#8221;)<\/p>\n<p data-start=\"566\" data-end=\"603\"><strong data-start=\"569\" data-end=\"601\">Mathematical Representation:<\/strong><\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">p\u2005\u200a\u27fa\u2005\u200aq=(p\u2192q)\u2227(q\u2192p)p \\iff q = (p \\rightarrow q) \\land (q \\rightarrow p)<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">p<\/span><span class=\"mrel\">\u27fa<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">q<\/span><span class=\"mrel\">=<\/span><\/span><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">p<\/span><span class=\"mrel\">\u2192<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">q<\/span><span class=\"mclose\">)<\/span><span class=\"mbin\">\u2227<\/span><\/span><span class=\"base\"><span class=\"mopen\">(<\/span><span class=\"mord mathnormal\">q<\/span><span class=\"mrel\">\u2192<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">p<\/span><span class=\"mclose\">)<\/span><\/span><\/span><\/span><\/span><\/p>\n<p data-start=\"665\" data-end=\"756\">\u0905\u0930\u094d\u0925\u093e\u0924: \u092f\u0926\u093f <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> \u0938\u0939\u0940 \u0939\u0948 \u0924\u094b <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> \u0938\u0939\u0940 \u0939\u094b\u0917\u093e \u0914\u0930 \u092f\u0926\u093f <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> \u0938\u0939\u0940 \u0939\u0948 \u0924\u094b <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> \u0938\u0939\u0940 \u0939\u094b\u0917\u093e\u0964<\/p>\n<p data-start=\"665\" data-end=\"756\"><strong data-start=\"766\" data-end=\"812\">\u00a02. Bi-Conditional Statement \u0915\u0947 Examples<\/strong><\/p>\n<h3 data-start=\"816\" data-end=\"839\"><strong data-start=\"820\" data-end=\"837\">\u00a0Example 1:<\/strong><\/h3>\n<p data-start=\"840\" data-end=\"1026\"><strong data-start=\"843\" data-end=\"857\">Statement:<\/strong><br data-start=\"857\" data-end=\"860\" \/><em data-start=\"860\" data-end=\"917\">&#8220;A number is even if and only if it is divisible by 2.&#8221;<\/em><br data-start=\"917\" data-end=\"920\" \/><strong data-start=\"922\" data-end=\"944\">Mathematical Form:<\/strong><br data-start=\"944\" data-end=\"947\" \/>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;A number is even&#8221;<br data-start=\"979\" data-end=\"982\" \/>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;A number is divisible by 2&#8221;<\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">p\u2005\u200a\u27fa\u2005\u200aqp \\iff q<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">p<\/span><span class=\"mrel\">\u27fa<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">q<\/span><\/span><\/span><\/span><\/span><\/p>\n<p data-start=\"1044\" data-end=\"1065\"><strong data-start=\"1047\" data-end=\"1063\">Explanation:<\/strong><\/p>\n<ul data-start=\"1066\" data-end=\"1185\">\n<li data-start=\"1066\" data-end=\"1125\">\u092f\u0926\u093f \u0915\u094b\u0908 \u0938\u0902\u0916\u094d\u092f\u093e <strong data-start=\"1083\" data-end=\"1091\">even<\/strong> \u0939\u0948 \u0924\u094b \u0935\u0939 <strong data-start=\"1101\" data-end=\"1123\">2 \u0938\u0947 \u0935\u093f\u092d\u093e\u091c\u094d\u092f \u0939\u094b\u0917\u0940\u0964<\/strong><\/li>\n<li data-start=\"1126\" data-end=\"1185\">\u092f\u0926\u093f \u0915\u094b\u0908 \u0938\u0902\u0916\u094d\u092f\u093e <strong data-start=\"1143\" data-end=\"1159\">2 \u0938\u0947 \u0935\u093f\u092d\u093e\u091c\u094d\u092f<\/strong> \u0939\u0948 \u0924\u094b \u0935\u0939 <strong data-start=\"1169\" data-end=\"1183\">even \u0939\u094b\u0917\u0940\u0964<\/strong><\/li>\n<\/ul>\n<h3 data-start=\"1192\" data-end=\"1215\"><strong data-start=\"1196\" data-end=\"1213\">\u00a0Example 2:<\/strong><\/h3>\n<p data-start=\"1216\" data-end=\"1432\"><strong data-start=\"1219\" data-end=\"1233\">Statement:<\/strong><br data-start=\"1233\" data-end=\"1236\" \/><em data-start=\"1236\" data-end=\"1305\">&#8220;A triangle is equilateral if and only if all its sides are equal.&#8221;<\/em><br data-start=\"1305\" data-end=\"1308\" \/><strong data-start=\"1310\" data-end=\"1332\">Mathematical Form:<\/strong><br data-start=\"1332\" data-end=\"1335\" \/>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;A triangle is equilateral&#8221;<br data-start=\"1376\" data-end=\"1379\" \/>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;All sides of the triangle are equal&#8221;<\/p>\n<p><span class=\"katex-display\"><span class=\"katex\"><span class=\"katex-mathml\">p\u2005\u200a\u27fa\u2005\u200aqp \\iff q<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">p<\/span><span class=\"mrel\">\u27fa<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">q<\/span><\/span><\/span><\/span><\/span><\/p>\n<p data-start=\"1450\" data-end=\"1471\"><strong data-start=\"1453\" data-end=\"1469\">Explanation:<\/strong><\/p>\n<ul data-start=\"1472\" data-end=\"1600\">\n<li data-start=\"1472\" data-end=\"1532\">\u092f\u0926\u093f <strong data-start=\"1478\" data-end=\"1501\">\u0924\u0940\u0928 \u092d\u0941\u091c\u093e\u090f\u0901 \u0938\u092e\u093e\u0928 \u0939\u0948\u0902<\/strong>, \u0924\u094b <strong data-start=\"1506\" data-end=\"1530\">\u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0938\u092e\u092c\u093e\u0939\u0941 \u0939\u094b\u0917\u093e\u0964<\/strong><\/li>\n<li data-start=\"1533\" data-end=\"1600\">\u092f\u0926\u093f <strong data-start=\"1539\" data-end=\"1560\">\u0924\u094d\u0930\u093f\u092d\u0941\u091c \u0938\u092e\u092c\u093e\u0939\u0941 \u0939\u0948<\/strong>, \u0924\u094b \u0909\u0938\u0915\u0940 <strong data-start=\"1570\" data-end=\"1598\">\u0924\u0940\u0928\u094b\u0902 \u092d\u0941\u091c\u093e\u090f\u0901 \u0938\u092e\u093e\u0928 \u0939\u094b\u0902\u0917\u0940\u0964<\/strong><\/li>\n<\/ul>\n<h3 data-start=\"1607\" data-end=\"1661\"><strong data-start=\"1610\" data-end=\"1659\">\u00a03. Bi-Conditional Statement \u0915\u0940 Truth Table<\/strong><\/h3>\n<table data-start=\"1663\" data-end=\"1867\">\n<thead data-start=\"1663\" data-end=\"1749\">\n<tr data-start=\"1663\" data-end=\"1749\">\n<th data-start=\"1663\" data-end=\"1673\"><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=\"1673\" data-end=\"1683\"><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=\"1683\" data-end=\"1707\"><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<th data-start=\"1707\" data-end=\"1731\"><span class=\"katex\"><span class=\"katex-mathml\">q\u2192pq \\rightarrow p<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">q<\/span><span class=\"mrel\">\u2192<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">p<\/span><\/span><\/span><\/span><\/th>\n<th data-start=\"1731\" data-end=\"1749\"><span class=\"katex\"><span class=\"katex-mathml\">p\u2005\u200a\u27fa\u2005\u200aqp \\iff q<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">p<\/span><span class=\"mrel\">\u27fa<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">q<\/span><\/span><\/span><\/span><\/th>\n<\/tr>\n<\/thead>\n<tbody data-start=\"1772\" data-end=\"1867\">\n<tr data-start=\"1772\" data-end=\"1795\">\n<td>T<\/td>\n<td>T<\/td>\n<td>T<\/td>\n<td>T<\/td>\n<td>\u00a0T<\/td>\n<\/tr>\n<tr data-start=\"1796\" data-end=\"1819\">\n<td>T<\/td>\n<td>F<\/td>\n<td>F<\/td>\n<td>T<\/td>\n<td>\u00a0F<\/td>\n<\/tr>\n<tr data-start=\"1820\" data-end=\"1843\">\n<td>F<\/td>\n<td>T<\/td>\n<td>T<\/td>\n<td>F<\/td>\n<td>\u00a0F<\/td>\n<\/tr>\n<tr data-start=\"1844\" data-end=\"1867\">\n<td>F<\/td>\n<td>F<\/td>\n<td>T<\/td>\n<td>T<\/td>\n<td>T<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p data-start=\"1869\" data-end=\"1990\"><strong data-start=\"1872\" data-end=\"1885\">\u0928\u093f\u0937\u094d\u0915\u0930\u094d\u0937:<\/strong><br data-start=\"1885\" data-end=\"1888\" \/>Bi-Conditional Statement \u0915\u0947\u0935\u0932 <strong data-start=\"1918\" data-end=\"1988\">\u0924\u092c TRUE \u0939\u094b\u0917\u093e \u091c\u092c \u0926\u094b\u0928\u094b\u0902 \u0938\u094d\u091f\u0947\u091f\u092e\u0947\u0902\u091f\u094d\u0938 \u090f\u0915 \u0938\u093e\u0925 TRUE \u092f\u093e \u090f\u0915 \u0938\u093e\u0925 FALSE \u0939\u094b\u0902\u0964<\/strong><\/p>\n<h3 data-start=\"1997\" data-end=\"2050\"><strong data-start=\"2000\" data-end=\"2048\">\u00a04. GATE PYQs on Bi-Conditional Statements<\/strong><\/h3>\n<p data-start=\"2052\" data-end=\"2357\"><strong data-start=\"2055\" data-end=\"2062\">Q1:<\/strong> \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u092e\u0947\u0902 \u0938\u0947 \u0915\u094c\u0928-\u0938\u093e \u0926\u094d\u0935\u093f-\u0936\u0930\u094d\u0924\u0940\u092f \u0915\u0925\u0928 \u0939\u0948?<br data-start=\"2107\" data-end=\"2110\" \/>\u00a0(a) &#8220;A number is prime if and only if it has exactly two divisors.&#8221;<br data-start=\"2179\" data-end=\"2182\" \/>(b) &#8220;If a number is prime, then it has exactly two divisors.&#8221;<br data-start=\"2243\" data-end=\"2246\" \/>(c) &#8220;If a number has exactly two divisors, then it is prime.&#8221;<br data-start=\"2307\" data-end=\"2310\" \/>(d) &#8220;A prime number is always an odd number.&#8221;<\/p>\n<p data-start=\"2359\" data-end=\"2429\"><strong data-start=\"2362\" data-end=\"2373\">Answer:<\/strong> (a) \u0915\u094d\u092f\u094b\u0902\u0915\u093f \u092f\u0939 <strong data-start=\"2389\" data-end=\"2413\">IFF (Bi-Conditional)<\/strong> \u0938\u094d\u091f\u0947\u091f\u092e\u0947\u0902\u091f \u0939\u0948\u0964<\/p>\n<h3 data-start=\"2436\" data-end=\"2472\"><strong data-start=\"2439\" data-end=\"2470\">\u00a05. \u0928\u093f\u0937\u094d\u0915\u0930\u094d\u0937 (Conclusion)<\/strong><\/h3>\n<p data-start=\"2473\" data-end=\"2725\"><strong data-start=\"2475\" data-end=\"2542\">Bi-Conditional Statement \u0915\u094b &#8220;If and Only If&#8221; (IFF) \u0915\u0939\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964<\/strong><br data-start=\"2542\" data-end=\"2545\" \/><strong data-start=\"2547\" data-end=\"2558\">Symbol:<\/strong> <span class=\"katex\"><span class=\"katex-mathml\">p\u2005\u200a\u27fa\u2005\u200aqp \\iff q<\/span><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">p<\/span><span class=\"mrel\">\u27fa<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">q<\/span><\/span><\/span><\/span><br data-start=\"2573\" data-end=\"2576\" \/><strong data-start=\"2578\" data-end=\"2651\">TRUE \u0924\u092d\u0940 \u0939\u094b\u0917\u093e \u091c\u092c \u0926\u094b\u0928\u094b\u0902 \u0938\u094d\u091f\u0947\u091f\u092e\u0947\u0902\u091f\u094d\u0938 (p \u0914\u0930 q) \u090f\u0915 \u0938\u093e\u0925 TRUE \u092f\u093e FALSE \u0939\u094b\u0902\u0964<\/strong><br data-start=\"2651\" data-end=\"2654\" \/><strong data-start=\"2656\" data-end=\"2723\">GATE, UGC-NET, \u0914\u0930 PSU Exams \u092e\u0947\u0902 \u0907\u0938 \u091f\u0949\u092a\u093f\u0915 \u092a\u0930 \u0938\u0935\u093e\u0932 \u092a\u0942\u091b\u0947 \u091c\u093e\u0924\u0947 \u0939\u0948\u0902\u0964<\/strong><\/p>\n<p data-start=\"2727\" data-end=\"2807\" data-is-last-node=\"\" data-is-only-node=\"\">\u00a0<strong data-start=\"2730\" data-end=\"2807\" data-is-last-node=\"\">\u0915\u094d\u092f\u093e \u0906\u092a Bi-Conditional Statements \u0938\u0947 \u091c\u0941\u0921\u093c\u0947 \u0914\u0930 \u0938\u0935\u093e\u0932 \u092f\u093e \u0928\u094b\u091f\u094d\u0938 \u091a\u093e\u0939\u0924\u0947 \u0939\u0948\u0902?<\/strong><\/p>\n<h3 data-start=\"2727\" data-end=\"2807\"><a href=\"https:\/\/www2.cs.uh.edu\/~arjun\/courses\/ds\/DiscMaths4CompSc.pdf\" target=\"_blank\" rel=\"noopener\">Day 04part 10- Discrete mathematics for gate in Hindi &#8211; Bi-conditional or if and only if statements.<\/a><\/h3>\n<h3 class=\"LC20lb MBeuO DKV0Md\"><a href=\"https:\/\/niamt.ac.in\/WriteReadData\/Mathematics%20(Discrete%20Structure).pdf\" target=\"_blank\" rel=\"noopener\">Mathematics (Discrete Structure).pdf<\/a><\/h3>\n<h3 class=\"LC20lb MBeuO DKV0Md\"><a href=\"https:\/\/dpvipracollege.ac.in\/wp-content\/uploads\/2023\/01\/Discrete-Mathematical-Structures-2nd-Ed.pdf\" target=\"_blank\" rel=\"noopener\">Discrete Mathematical Structures<\/a><\/h3>\n<h3 class=\"LC20lb MBeuO DKV0Md\"><a href=\"https:\/\/www.vidyalankar.org\/infinite\/assets\/docs\/study-material\/cse-module-10.pdf\" target=\"_blank\" rel=\"noopener\">Discrete Mathematics INDEX<\/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<h3 class=\"LC20lb MBeuO DKV0Md\"><a href=\"https:\/\/mrcet.com\/downloads\/digital_notes\/IT\/CSE%20_(R22)_2-2_DM%20DIGITAL%20NOTES.pdf\" target=\"_blank\" rel=\"noopener\">Discrete Mathematics<\/a><\/h3>\n<p>Here\u2019s a detailed summary and explanation for:<\/p>\n<h2>\ud83c\udf93 <strong>Day 04 Part 10 \u2013 Discrete Mathematics for GATE in Hindi<\/strong><\/h2>\n<h3>Topic: <strong>Bi-Conditional \/ \u201cIf and Only If\u201d Statements<\/strong><\/h3>\n<p>(Language: Hindi + English mix for GATE aspirants)<\/p>\n<hr \/>\n<h2>\ud83d\udd39 <strong>Bi-Conditional Statement \u0915\u094d\u092f\u093e \u0939\u094b\u0924\u093e \u0939\u0948?<\/strong><\/h2>\n<p>Bi-conditional statement \u090f\u0915 \u0910\u0938\u093e logical statement \u0939\u094b\u0924\u093e \u0939\u0948 \u091c\u093f\u0938\u092e\u0947\u0902 \u0926\u094b propositions \u0915\u0947 \u092c\u0940\u091a <strong>\u201cif and only if\u201d (iff)<\/strong> \u0938\u0902\u092c\u0902\u0927 \u0939\u094b\u0924\u093e \u0939\u0948\u0964<\/p>\n<p>\ud83d\udcd8 <strong>Symbol:<\/strong><br \/>\n<code>P \u21d4 Q<\/code> (P if and only if Q)<\/p>\n<p>\ud83d\udccc \u0907\u0938\u0915\u093e \u0905\u0930\u094d\u0925 \u0939\u0948:<br \/>\n<strong>P \u0924\u092d\u0940 \u0938\u0924\u094d\u092f \u0939\u0948 \u091c\u092c Q \u0938\u0924\u094d\u092f \u0939\u0948, \u0914\u0930 Q \u0924\u092d\u0940 \u0938\u0924\u094d\u092f \u0939\u0948 \u091c\u092c P \u0938\u0924\u094d\u092f \u0939\u0948\u0964<\/strong><\/p>\n<hr \/>\n<h2>\u2705 <strong>Bi-conditional \u0915\u093e Truth Table:<\/strong><\/h2>\n<table>\n<thead>\n<tr>\n<th>P<\/th>\n<th>Q<\/th>\n<th>P \u21d4 Q<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>T<\/td>\n<td>T<\/td>\n<td>T<\/td>\n<\/tr>\n<tr>\n<td>T<\/td>\n<td>F<\/td>\n<td>F<\/td>\n<\/tr>\n<tr>\n<td>F<\/td>\n<td>T<\/td>\n<td>F<\/td>\n<\/tr>\n<tr>\n<td>F<\/td>\n<td>F<\/td>\n<td>T<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>\ud83d\udc49 <strong>\u0938\u093f\u0930\u094d\u092b \u0924\u092d\u0940 True \u0939\u094b\u0924\u093e \u0939\u0948 \u091c\u092c \u0926\u094b\u0928\u094b\u0902 \u090f\u0915 \u091c\u0948\u0938\u0947 \u0939\u094b\u0902<\/strong> (\u092f\u093e \u0924\u094b \u0926\u094b\u0928\u094b\u0902 True \u092f\u093e \u0926\u094b\u0928\u094b\u0902 False)<\/p>\n<hr \/>\n<h2>\ud83c\udfaf <strong>GATE \u092e\u0947\u0902 \u092a\u0942\u091b\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948:<\/strong><\/h2>\n<blockquote><p><strong>Q. \u092f\u0926\u093f P \u21d4 Q \u0938\u0924\u094d\u092f \u0939\u0948, \u0924\u094b \u0915\u094c\u0928-\u0915\u094c\u0928 \u0938\u0947 logical equivalences \u0938\u0939\u0940 \u0939\u094b\u0902\u0917\u0947?<\/strong><\/p><\/blockquote>\n<p>\u2714\ufe0f <code>P \u21d4 Q<\/code> \u0915\u093e \u092e\u0924\u0932\u092c \u0939\u094b\u0924\u093e \u0939\u0948:<br \/>\n<strong>(P \u2192 Q) \u2227 (Q \u2192 P)<\/strong><br \/>\n\u092f\u093e\u0928\u093f \u090f\u0915 \u0939\u0940 \u0938\u092e\u092f \u092a\u0930 \u0926\u094b\u0928\u094b\u0902 \u090f\u0915-\u0926\u0942\u0938\u0930\u0947 \u0915\u094b imply \u0915\u0930\u0947\u0902\u0964<\/p>\n<hr \/>\n<h2>\ud83e\udde0 <strong>Examples (With Hindi Explanation):<\/strong><\/h2>\n<h3>Example 1:<\/h3>\n<p><strong>P:<\/strong> You will pass the exam<br \/>\n<strong>Q:<\/strong> You study sincerely<\/p>\n<p>\ud83d\udccc Statement:<br \/>\n\ud83d\udc49 &#8220;You will pass the exam <strong>if and only if<\/strong> you study sincerely.&#8221;<br \/>\n\ud83d\udd01 <strong>&#8220;Tum exam pass \u0915\u0930\u094b\u0917\u0947 \u0924\u092d\u0940 \u0914\u0930 \u0924\u092d\u0940 \u091c\u092c \u0924\u0941\u092e \u0908\u092e\u093e\u0928\u0926\u093e\u0930\u0940 \u0938\u0947 \u092a\u0922\u093c\u093e\u0908 \u0915\u0930\u094b\u0917\u0947\u0964&#8221;<\/strong><\/p>\n<p>Truth: \u092f\u0947 \u0924\u092d\u0940 \u0938\u091a \u0939\u094b\u0917\u093e \u091c\u092c \u0926\u094b\u0928\u094b\u0902 P \u0914\u0930 Q \u090f\u0915 \u0938\u093e\u0925 \u0938\u0939\u0940 \u092f\u093e \u0917\u0932\u0924 \u0939\u094b\u0902\u0964<\/p>\n<hr \/>\n<h3>Example 2:<\/h3>\n<p><strong>P \u21d4 Q \u2261 (P \u2192 Q) \u2227 (Q \u2192 P)<\/strong><br \/>\nLogical equivalence form \u0939\u0948 \u091c\u094b GATE \u0915\u0947 MCQs \u092e\u0947\u0902 \u092a\u0942\u091b\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964<\/p>\n<hr \/>\n<h2>\ud83d\udccc Bi-conditional \u0915\u094b \u092f\u093e\u0926 \u0930\u0916\u0928\u0947 \u0915\u093e \u0924\u0930\u0940\u0915\u093e:<\/h2>\n<blockquote><p>&#8220;<strong>\u0926\u094b\u0928\u094b\u0902 \u0915\u093e \u092d\u093e\u0917\u094d\u092f \u090f\u0915 \u091c\u0948\u0938\u093e \u2013 \u092f\u093e \u0924\u094b \u0926\u094b\u0928\u094b\u0902 \u092a\u093e\u0938, \u092f\u093e \u0926\u094b\u0928\u094b\u0902 \u092b\u0947\u0932!<\/strong>&#8220;<\/p><\/blockquote>\n<hr \/>\n<h2>\ud83d\udd0d BONUS:<\/h2>\n<p>Would you like:<\/p>\n<ul>\n<li>\ud83d\udcdd Practice Questions (PDF) on Bi-conditional with Solutions<\/li>\n<li>\ud83c\udfa5 Video Lecture in Hindi<\/li>\n<li>\ud83d\udcd8 Formula Sheet for Discrete Mathematics<\/li>\n<\/ul>\n<p>\u092c\u0938 \u092c\u0924\u093e\u0907\u090f, \u092e\u0948\u0902 \u0924\u0941\u0930\u0902\u0924 \u0924\u0948\u092f\u093e\u0930 \u0915\u0930 \u0926\u0942\u0901\u0917\u093e!<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Day 04part 10- Discrete mathematics for gate in Hindi &#8211; Bi-conditional or if and only if statements. [fvplayer id=&#8221;203&#8243;] \u00a0Day 04 Part 10 &#8211; Discrete Mathematics for GATE in Hindi Bi-Conditional Statements (If and Only If &#8211; IFF) | \u0926\u094d\u0935\u093f-\u0936\u0930\u094d\u0924\u0940\u092f \u0915\u0925\u0928 Language: HindiTopic: Bi-Conditional StatementsPart: 10Exam Focus: GATE, UGC-NET, PSU Exams \u00a01. Bi-Conditional Statement (IFF) [&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-2988","post","type-post","status-publish","format-standard","hentry","category-discrete-mathematics"],"_links":{"self":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts\/2988","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=2988"}],"version-history":[{"count":0,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/posts\/2988\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/media?parent=2988"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/categories?post=2988"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.reilsolar.com\/pdf\/wp-json\/wp\/v2\/tags?post=2988"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}