{"id":68110,"date":"2021-08-31T14:15:00","date_gmt":"2021-08-31T08:45:00","guid":{"rendered":"https:\/\/www.kopykitab.com\/blog\/?p=68110"},"modified":"2021-08-31T14:15:29","modified_gmt":"2021-08-31T08:45:29","slug":"rd-sharma-solutions-class-11-maths-chapter-31-exercise-31-5","status":"publish","type":"post","link":"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-31-exercise-31-5\/","title":{"rendered":"RD Sharma Class 11 Solutions Chapter 31 Exercise 31.5 (Updated for 2021-22)"},"content":{"rendered":"\n<p><img class=\"alignnone size-full wp-image-121613\" src=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/RD-Sharma-Class-11-Solutions-Chapter-31-Exercise-31.5.jpg\" alt=\"RD Sharma Solutions Class 11 Maths Chapter 31 Exercise 31.5\" width=\"1200\" height=\"675\" srcset=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/RD-Sharma-Class-11-Solutions-Chapter-31-Exercise-31.5.jpg 1200w, https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/RD-Sharma-Class-11-Solutions-Chapter-31-Exercise-31.5-768x432.jpg 768w\" sizes=\"(max-width: 1200px) 100vw, 1200px\" \/><\/p>\n<p><strong>RD Sharma Solutions Class 11 Maths Chapter 31 Exercise 31.5:\u00a0<\/strong>Many statements of the form &#8220;if p then q,&#8221; &#8220;p only if q,&#8221; and &#8220;if and only if&#8221; can be found in mathematics. These statements are known as implications. Such statements will be discussed in this exercise. Subject matter experts prepare and review the <a href=\"https:\/\/www.kopykitab.com\/blog\/cbse-class-11-maths-rd-sharma-solutions\/\"><strong>RD Sharma Class 11 Solutions<\/strong><\/a>, which are then updated to reflect the latest syllabus. Students can refer to and download the <a href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-31-mathematical-reasoning\/\"><strong>RD Sharma Solutions Class 11 Maths Chapter 31<\/strong><\/a> Exercise 31.5 pdf from the URLs provided below.<\/p>\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_47_1 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"ez-toc-toggle-icon-1\"><label for=\"item-69d4aabd071eb\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;direction:ltr;\"><svg style=\"fill: #000000;color:#000000\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 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href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-31-exercise-31-5\/#download-rd-sharma-class-11-solutions-chapter-31-exercise-315-free-pdf\" title=\"Download RD Sharma Class 11 Solutions Chapter 31 Exercise 31.5 Free PDF\">Download RD Sharma Class 11 Solutions Chapter 31 Exercise 31.5 Free PDF<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-31-exercise-31-5\/#access-answers-to-rd-sharma-solutions-class-11-maths-chapter-31-exercise-315-important-question-with-answers\" title=\"Access answers to RD Sharma Solutions Class 11 Maths Chapter 31 Exercise 31.5- Important Question with Answers\">Access answers to RD Sharma Solutions Class 11 Maths Chapter 31 Exercise 31.5- Important Question with Answers<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-31-exercise-31-5\/#faqs-on-rd-sharma-solutions-class-11-maths-chapter-31-exercise-315\" title=\"FAQs on RD Sharma Solutions Class 11 Maths Chapter 31 Exercise 31.5\">FAQs on RD Sharma Solutions Class 11 Maths Chapter 31 Exercise 31.5<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-31-exercise-31-5\/#how-many-questions-are-there-in-rd-sharma-solutions-class-11-maths-chapter-31-exercise-315\" title=\"How many questions are there in RD Sharma Solutions Class 11 Maths Chapter 31 Exercise 31.5?\">How many questions are there in RD Sharma Solutions Class 11 Maths Chapter 31 Exercise 31.5?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-31-exercise-31-5\/#where-can-i-download-rd-sharma-solutions-class-11-maths-chapter-31-exercise-315-free-pdf\" title=\"Where can I download RD Sharma Solutions Class 11 Maths Chapter 31 Exercise 31.5 free PDF?\">Where can I download RD Sharma Solutions Class 11 Maths Chapter 31 Exercise 31.5 free PDF?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-31-exercise-31-5\/#what-are-the-benefits-of-using-kopykitab%e2%80%99s-rd-sharma-solutions-class-11-maths-chapter-31-exercise-315\" title=\"What are the benefits of using Kopykitab\u2019s RD Sharma Solutions Class 11 Maths Chapter 31 Exercise 31.5?\">What are the benefits of using Kopykitab\u2019s RD Sharma Solutions Class 11 Maths Chapter 31 Exercise 31.5?<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"download-rd-sharma-class-11-solutions-chapter-31-exercise-315-free-pdf\"><\/span>Download RD Sharma Class 11 Solutions Chapter 31 Exercise 31.5 Free PDF<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><a href=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/RD-Sharma-Solutions-Class-11-Maths-Chapter-31-Ex-31.5-1.pdf\">RD Sharma Solutions Class 11 Maths Chapter 31 Exercise 31.5<\/a><\/p>\n<div id=\"example1\" style=\"text-align: justify;\">\u00a0<\/div>\n<p style=\"text-align: justify;\"><style>\n.pdfobject-container { height: 800px;}<br \/>\n.pdfobject { border: 1px solid #666; }<br \/>\n<\/style><\/p>\n<p style=\"text-align: justify;\"><script src=\"https:\/\/www.kopykitab.com\/_utility\/js\/pdfobject.min.js\"><\/script><br \/><script>PDFObject.embed(\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/RD-Sharma-Solutions-Class-11-Maths-Chapter-31-Ex-31.5-1.pdf\", \"#example1\");<\/script><\/p>\n<h3><span class=\"ez-toc-section\" id=\"access-answers-to-rd-sharma-solutions-class-11-maths-chapter-31-exercise-315-important-question-with-answers\"><\/span>Access answers to RD Sharma Solutions Class 11 Maths Chapter 31 Exercise 31.5- Important Question with Answers<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<article>\n<p><strong>1. Write each of the following statements in the form \u201cif p, then q.\u201d<br \/>(i) You can access the website only if you pay a subscription fee.<br \/>(ii) There is a traffic jam whenever it rains.<br \/>(iii) It is necessary to have a passport to log on to the server.<br \/>(iv) It is necessary to be rich to be happy.<br \/>(v) The game is canceled only if it is raining.<br \/>(vi) It rains only if it is cold.<br \/>(vii) Whenever it rains, it is cold.<br \/>(viii) It never rains when it is cold.<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p><strong>(i)<\/strong>\u00a0If you access the website, then you pay a subscription fee.<\/p>\n<p><strong>(ii)<\/strong>\u00a0If it rains, then there is a traffic jam.<\/p>\n<p><br \/><strong>(iii)<\/strong> If you log on to the server, then you must have a passport.<\/p>\n<p><br \/><strong>(iv)<\/strong>\u00a0If he is happy, then he is rich.<\/p>\n<p><br \/><strong>(v)<\/strong>\u00a0If it is raining, then the game is canceled.<\/p>\n<p><br \/><strong>(vi)<\/strong>\u00a0If it rains, then it is cold.<\/p>\n<p><br \/><strong>(vii)<\/strong>\u00a0If it rains, then it is cold.<\/p>\n<p><strong>(viii)<\/strong>\u00a0If it is cold, then it never rains.<\/p>\n<p><strong>2. State the converse and contrapositive of each of the following statements:<br \/>(i) If it is hot outside, then you feel thirsty.<\/strong><\/p>\n<p><strong>(ii) I go to a beach whenever it is a sunny day.<\/strong><\/p>\n<p><strong>(iii) A positive integer is prime only if it has no divisions other than 1 and itself.<\/strong><\/p>\n<p><strong>(iv) If you live in Delhi, then you have winter clothes.<\/strong><\/p>\n<p><strong>(v) If a quadrilateral is a parallelogram, then its diagonals bisect each other.<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p><strong>(i)\u00a0<\/strong>If it is hot outside, then you feel thirsty<strong>.<\/strong><\/p>\n<p>Converse: If you feel thirsty, then it is hot outside.<\/p>\n<p><br \/>Contrapositive: If you do not feel thirsty, then it is not hot outside.<\/p>\n<p><strong>(ii)\u00a0<\/strong>I go to a beach whenever it is a sunny day.<\/p>\n<p>Converse: If I go to a beach, then it is a sunny day.<\/p>\n<p><br \/>Contrapositive: If I do not go to a beach, then it is not a sunny day.<\/p>\n<p><strong>(iii)\u00a0<\/strong>A positive integer is prime only if it has no divisions other than 1 and itself.<\/p>\n<p>Converse: If an integer has no divisor other than 1 and itself, then it is prime.<\/p>\n<p><br \/>Contrapositive: If an integer has some divisor other than 1 and itself, then it is prime.<\/p>\n<p><strong>(iv)\u00a0<\/strong>If you live in Delhi, then you have winter clothes.<\/p>\n<p>Converse: If you have winter clothes, then you live in Delhi.<\/p>\n<p><br \/>Contrapositive: If you do not have winter clothes, then you do not live in Delhi.<\/p>\n<p><strong>(v)\u00a0<\/strong>If a quadrilateral is a parallelogram, then its diagonals bisect each other.<\/p>\n<p>Converse: If the diagonals of a quadrilateral bisect each other, then it is a parallelogram.<\/p>\n<p><br \/>Contrapositive: If the diagonals of a quadrilateral do not bisect each other, then the quadrilateral is not a parallelogram.<\/p>\n<p><strong>RD Sharma Solutions Class 11 Maths Chapter 31 Exercise 31.5 Q3.<\/strong><\/p>\n<p><strong>3. Rewrite each of the following statements in the form \u201cp if and only if q.\u201d<br \/>(i) p: If you watch television, then your mind is free, and if your mind is free, then you watch television.<br \/>(ii) q: If a quadrilateral is equiangular, then it is a rectangle, and if a quadrilateral is a rectangle, then it is equiangular.<br \/>(iii) r: For you to get an A grade, it is necessary and sufficient that you do all the homework you regularly.<br \/>(iv) s: If a tumbler is half empty, then it is half full, and if a tumbler is half full, then it is half empty.<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p><strong>(i)<\/strong>\u00a0You watch television if and only if your mind is free.<\/p>\n<p><strong>(ii)<\/strong>\u00a0A quadrilateral is a rectangle if and only if it is equiangular.<\/p>\n<p><br \/><strong>(iii)<\/strong>\u00a0You get an A grade if and only if you do all the homework regularly.<\/p>\n<p><br \/><strong>(iv)<\/strong>\u00a0A tumbler is half empty if and only if it is half full.<\/p>\n<p><strong>4.<\/strong>\u00a0<strong>Determine the Contrapositive of each of the following statements:<br \/>(i) If Mohan is a poet, then he is poor.<br \/>(ii) Only if Max studies will he pass the test.<br \/>(iii) If she works, she will earn money.<br \/>(iv) If it snows, then they do not drive the car.<br \/>(v) It never rains when it is cold.<br \/>(vi) If Ravish skis, then it snowed.<br \/>(vii) If x is less than zero, then x is not positive.<br \/>(viii) If he has courage he will win.<br \/>(ix) It is necessary to be strong to be a sailor.<br \/>(x) Only if he does not tire will he win.<br \/>(xi) If x is an integer and x<sup>2<\/sup>\u00a0is odd, then x is odd.<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p><strong>(i)<\/strong>\u00a0If Mohan is a poet, then he is poor.<\/p>\n<p>Contrapositive: If Mohan is not poor, then he is not a poet.<\/p>\n<p><br \/><strong>(ii)<\/strong>\u00a0Only if Max studies will he pass the test.<\/p>\n<p>Contrapositive: If Max does not study, then he will not pass the test.<\/p>\n<p><br \/><strong>(iii)<\/strong>\u00a0If she works, she will earn money.<\/p>\n<p>Contrapositive: If she does not earn money, then she does not work.<\/p>\n<p><br \/><strong>(iv)<\/strong>\u00a0If it snows, then they do not drive the car.<\/p>\n<p>Contrapositive: If then they do not drive the car, then there is no snow.<\/p>\n<p><br \/><strong>(v)<\/strong>\u00a0It never rains when it is cold.<\/p>\n<p>Contrapositive: If it rains, then it is not cold.<\/p>\n<p><strong>(vi)<\/strong>\u00a0If Ravish skis, then it snowed.<\/p>\n<p>Contrapositive: If it did not snow, then Ravish will not ski.<\/p>\n<p><br \/><strong>(vii)<\/strong>\u00a0If x is less than zero, then x is not positive.<\/p>\n<p>Contrapositive: If x is positive, then x is not less than zero.<\/p>\n<p><br \/><strong>(viii)<\/strong>\u00a0If he has courage he will win.<\/p>\n<p>Contrapositive: If he does not win, then he does not have courage.<\/p>\n<p><strong>(ix)<\/strong> It is necessary to be strong to be a sailor.<\/p>\n<p>Contrapositive: If he is not strong, then he is not a sailor<\/p>\n<p><br \/><strong>(x)<\/strong>\u00a0Only if he does not tire will he win.<\/p>\n<p>Contrapositive: If he tries, then he will not win.<\/p>\n<p><br \/><strong>(xi)<\/strong>\u00a0If x is an integer and x<sup>2<\/sup>\u00a0is odd, then x is odd.<\/p>\n<p>Contrapositive: If x is even, then x<sup>2<\/sup>\u00a0is even.<\/p>\n<p>We have provided complete details of RD Sharma Solutions Class 11\u00a0Chapter 31 Exercise 31.5. If you have any queries related to <a href=\"https:\/\/www.cbse.gov.in\/\" target=\"_blank\" rel=\"noopener\"><strong>CBSE<\/strong><\/a>\u00a0Class 11, feel free to ask us in the comment section below.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"faqs-on-rd-sharma-solutions-class-11-maths-chapter-31-exercise-315\"><\/span>FAQs on RD Sharma Solutions Class 11 Maths Chapter 31 Exercise 31.5<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<\/article>\n\n\n<div id=\"rank-math-faq\" class=\"rank-math-block\">\n<div class=\"rank-math-list \">\n<div id=\"faq-question-1630397512055\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"how-many-questions-are-there-in-rd-sharma-solutions-class-11-maths-chapter-31-exercise-315\"><\/span>How many questions are there in RD Sharma Solutions Class 11 Maths Chapter 31 Exercise 31.5?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>There are a total of 4 questions in RD Sharma Solutions Class 11 Maths Chapter 31 Exercise 31.5.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1630397612117\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"where-can-i-download-rd-sharma-solutions-class-11-maths-chapter-31-exercise-315-free-pdf\"><\/span>Where can I download RD Sharma Solutions Class 11 Maths Chapter 31 Exercise 31.5 free PDF?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>You can download RD Sharma Solutions Class 11 Maths Chapter 31 Exercise 31.5 free PDF from the above article.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1630397612970\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"what-are-the-benefits-of-using-kopykitab%e2%80%99s-rd-sharma-solutions-class-11-maths-chapter-31-exercise-315\"><\/span>What are the benefits of using Kopykitab\u2019s RD Sharma Solutions Class 11 Maths Chapter 31 Exercise 31.5?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>The following are some of the benefits of using Kopykitab\u2019s RD Sharma Solutions Class 11 Maths Chapter 31 Exercise 31.5:<br \/>1. Correct answers according to the last CBSE guidelines and syllabus.<br \/>2. The RD Sharma Solutions Class 11 Maths Chapter 31 Exercise 31.5 is written in simple language to assist students in their board examination, &amp; competitive examination preparation.<\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>RD Sharma Solutions Class 11 Maths Chapter 31 Exercise 31.5:\u00a0Many statements of the form &#8220;if p then q,&#8221; &#8220;p only if q,&#8221; and &#8220;if and only if&#8221; can be found in mathematics. These statements are known as implications. Such statements will be discussed in this exercise. Subject matter experts prepare and review the RD Sharma &#8230; <a title=\"RD Sharma Class 11 Solutions Chapter 31 Exercise 31.5 (Updated for 2021-22)\" class=\"read-more\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-31-exercise-31-5\/\" aria-label=\"More on RD Sharma Class 11 Solutions Chapter 31 Exercise 31.5 (Updated for 2021-22)\">Read more<\/a><\/p>\n","protected":false},"author":238,"featured_media":121613,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"","fifu_image_alt":""},"categories":[73411,2985,73410],"tags":[3428,73334,73564,4388],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/68110"}],"collection":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/users\/238"}],"replies":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/comments?post=68110"}],"version-history":[{"count":4,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/68110\/revisions"}],"predecessor-version":[{"id":121706,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/68110\/revisions\/121706"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media\/121613"}],"wp:attachment":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media?parent=68110"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/categories?post=68110"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/tags?post=68110"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}