{"id":68107,"date":"2021-08-31T12:16:00","date_gmt":"2021-08-31T06:46:00","guid":{"rendered":"https:\/\/www.kopykitab.com\/blog\/?p=68107"},"modified":"2021-08-31T14:14:30","modified_gmt":"2021-08-31T08:44:30","slug":"rd-sharma-solutions-class-11-maths-chapter-31-exercise-31-2","status":"publish","type":"post","link":"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-31-exercise-31-2\/","title":{"rendered":"RD Sharma Class 11 Solutions Chapter 31 Exercise 31.2 (Updated for 2021-22)"},"content":{"rendered":"\n<p><img class=\"alignnone size-full wp-image-121606\" src=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/RD-Sharma-Class-11-Solutions-Chapter-31-Exercise-31.2.jpg\" alt=\"RD Sharma Solutions Class 11 Maths Chapter 31 Exercise 31.2\" width=\"1200\" height=\"675\" srcset=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/RD-Sharma-Class-11-Solutions-Chapter-31-Exercise-31.2.jpg 1200w, https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/RD-Sharma-Class-11-Solutions-Chapter-31-Exercise-31.2-768x432.jpg 768w\" sizes=\"(max-width: 1200px) 100vw, 1200px\" \/><\/p>\n<p><strong>RD Sharma Solutions Class 11 Maths Chapter 31 Exercise 31.2:\u00a0<\/strong>In this exercise, we&#8217;ll look at the concept of negation in relation to a statement. The solutions are created by Kopykitab&#8217;s experts who have extensive experience in the field of education. The primary goal of providing <a href=\"https:\/\/www.kopykitab.com\/blog\/cbse-class-11-maths-rd-sharma-solutions\/\"><strong>RD Sharma Class 11 Solutions<\/strong><\/a> is to assist students, regardless of their intellect level. The solutions are written in simple language to assist students grasp the concepts and perform well on the yearly exam. Students can get <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 31.2 by clicking on the links below and practising offline.<\/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-69d31903cd333\" 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-31-2\/#download-rd-sharma-class-11-solutions-chapter-31-exercise-312-free-pdf\" title=\"Download RD Sharma Class 11 Solutions Chapter 31 Exercise 31.2 Free PDF\">Download RD Sharma Class 11 Solutions Chapter 31 Exercise 31.2 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-31-2\/#access-answers-to-rd-sharma-solutions-class-11-maths-chapter-31-exercise-312-important-question-with-answers\" title=\"Access answers to RD Sharma Solutions Class 11 Maths Chapter 31 Exercise 31.2- Important Question with Answers\">Access answers to RD Sharma Solutions Class 11 Maths Chapter 31 Exercise 31.2- Important Question with Answers<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link 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href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-31-exercise-31-2\/#where-can-i-download-rd-sharma-solutions-class-11-maths-chapter-31-exercise-312-free-pdf\" title=\"Where can I download RD Sharma Solutions Class 11 Maths Chapter 31 Exercise 31.2 free PDF?\">Where can I download RD Sharma Solutions Class 11 Maths Chapter 31 Exercise 31.2 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-31-2\/#what-are-the-benefits-of-using-kopykitab%e2%80%99s-rd-sharma-solutions-class-11-maths-chapter-31-exercise-312\" title=\"What are the benefits of using Kopykitab\u2019s RD Sharma Solutions Class 11 Maths Chapter 31 Exercise 31.2?\">What are the benefits of using Kopykitab\u2019s RD Sharma Solutions Class 11 Maths Chapter 31 Exercise 31.2?<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"download-rd-sharma-class-11-solutions-chapter-31-exercise-312-free-pdf\"><\/span>Download RD Sharma Class 11 Solutions Chapter 31 Exercise 31.2 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-31.2-1.pdf\">RD Sharma Solutions Class 11 Maths Chapter 31 Exercise 31.2<\/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-31.2-1.pdf\", \"#example1\");<\/script><\/p>\n<h3><span class=\"ez-toc-section\" id=\"access-answers-to-rd-sharma-solutions-class-11-maths-chapter-31-exercise-312-important-question-with-answers\"><\/span>Access answers to RD Sharma Solutions Class 11 Maths Chapter 31 Exercise 31.2- Important Question with Answers<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>1. Write the negation of the following statement:<br \/>(i) Bangalore is the capital of Karnataka.<\/strong><\/p>\n<p><strong>(ii) It rained on July 4, 2005.<\/strong><\/p>\n<p><strong>(iii) Ravish is honest.<\/strong><\/p>\n<p><strong>(iv) The earth is round.<\/strong><\/p>\n<p><strong>(v) The sun is cold.<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p><strong>(i)\u00a0<\/strong>Bangalore is the capital of Karnataka.<\/p>\n<p>The negation of the statement is:<\/p>\n<p>It is false that \u201cBangalore is the capital of Karnataka.\u201d<\/p>\n<p>Or<\/p>\n<p>\u201cBangalore is not the capital of Karnataka.\u201d<\/p>\n<p><strong>(ii)\u00a0<\/strong>It rained on July 4, 2005.<\/p>\n<p>The negation of the statement is:<\/p>\n<p>It is false that \u201cIt rained on July 4, 2005\u201d.<\/p>\n<p>Or<\/p>\n<p>\u201cIt did not rain on July 4, 2005\u201d.<\/p>\n<p><strong>(iii)\u00a0<\/strong>Ravish is honest.<\/p>\n<p>The negation of the statement is:<\/p>\n<p>It is false that \u201cRavish is honest.\u201d<\/p>\n<p>Or<\/p>\n<p>\u201cRavish is not honest.\u201d<\/p>\n<p><strong>(iv)\u00a0<\/strong>The earth is round.<\/p>\n<p>The negation of the statement is:<\/p>\n<p>It is false that \u201cThe earth is round.\u201d<\/p>\n<p>Or<\/p>\n<p>\u201cThe earth is not round.\u201d<\/p>\n<p><strong>(v)\u00a0<\/strong>The sun is cold.<\/p>\n<p>The negation of the statement is:<\/p>\n<p>It is false that \u201cThe sun is cold.\u201d<\/p>\n<p>Or<\/p>\n<p>\u201cThe sun is not cold.\u201d<\/p>\n<p><strong>2. (i) All birds sing.<\/strong><\/p>\n<p><strong>(ii) Some even integers are prime.<\/strong><\/p>\n<p><strong>(iii) There is a complex number that is not a real number.<\/strong><\/p>\n<p><strong>(iv) I will not go to school.<\/strong><\/p>\n<p><strong>(v) Both the diagonals of a rectangle have the same length.<\/strong><\/p>\n<p><strong>(vi) All policemen are thieves.<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p><strong>(i)\u00a0<\/strong>All birds sing.<\/p>\n<p>The negation of the statement is:<\/p>\n<p>It is false that \u201cAll birds sing.\u201d<\/p>\n<p>Or<\/p>\n<p>\u201cAll birds do not sing.\u201d<\/p>\n<p><strong>(ii)\u00a0<\/strong>Some even integers are prime.<\/p>\n<p>The negation of the statement is:<\/p>\n<p>It is false that \u201ceven integers are prime.\u201d<\/p>\n<p>Or<\/p>\n<p>\u201cNot every even integer is prime.\u201d<\/p>\n<p><strong>(iii)\u00a0<\/strong>There is a complex number that is not a real number.<\/p>\n<p>The negation of the statement is:<\/p>\n<p>It is false that \u201ccomplex numbers are not a real number.\u201d<\/p>\n<p>Or<\/p>\n<p>\u201cAll complex numbers are real numbers.\u201d<\/p>\n<p><strong>(iv)\u00a0<\/strong>I will not go to school.<\/p>\n<p>The negation of the statement is:<\/p>\n<p>\u201cI will go to school.\u201d<\/p>\n<p><strong>(v)\u00a0<\/strong>Both the diagonals of a rectangle have the same length.<\/p>\n<p>The negation of the statement is:<\/p>\n<p>\u201cThere is at least one rectangle whose both diagonals do not have the same length.\u201d<\/p>\n<p><strong>(vi)\u00a0<\/strong>All policemen are thieves.<\/p>\n<p>The negation of the statement is:<\/p>\n<p>\u201cNo policemen are thieves\u201d.<\/p>\n<p><strong>3. Are the following pairs of statements are a negation of each other:<br \/>(i) The number x is not a rational number.<br \/>The number x is not an irrational number.<br \/>(ii) The number x is not a rational number.<br \/>The number x is an irrational number.<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p><strong>(i)<\/strong>\u00a0The number x is not a rational number.<\/p>\n<p>\u201cThe number x is an irrational number.\u201d<\/p>\n<p>Since the statement \u201cThe number x is not a rational number.\u201d Is a negation of the first statement.<\/p>\n<p><br \/><strong>(ii)<\/strong>\u00a0The number x is not a rational number.<\/p>\n<p>\u201cThe number x is an irrational number.\u201d<\/p>\n<p>Since the statement \u201cThe number x is a rational number.\u201d Is not a negation of the first statement.<\/p>\n<p><strong>4. Write the negation of the following statements:<\/strong><\/p>\n<p><strong>(i) p: For every positive real number x, the number (x \u2013 1) is also positive.<\/strong><\/p>\n<p><strong>(ii) q: For every real number x, either x &gt; 1 or x &lt; 1.<\/strong><\/p>\n<p><strong>(iii) r: There exists a number x such that 0 &lt; x &lt; 1.<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p><strong>(i)\u00a0<\/strong>p : For every positive real number x, the number (x \u2013 1) is also positive.<\/p>\n<p>The negation of the statement:<\/p>\n<p>p: For every positive real number x, the number (x \u2013 1) is also positive.<\/p>\n<p>is<\/p>\n<p>~p: There exists a positive real number x, such that the number (x \u2013 1) is not positive.<\/p>\n<p><strong>(ii)\u00a0<\/strong>q:For every real number x, either x &gt; 1 or x &lt; 1.<\/p>\n<p>The negation of the statement:<\/p>\n<p>q: For every real number x, either x &gt; 1 or x &lt; 1.<\/p>\n<p>is<\/p>\n<p>~q: There exists a real number such that neither x&gt;1 nor x&lt;1.<\/p>\n<p><strong>(iii)\u00a0<\/strong>r: There exists a number x such that 0 &lt; x &lt; 1.<\/p>\n<p>The negation of the statement:<\/p>\n<p>r: There exists a number x such that 0 &lt; x &lt; 1.<\/p>\n<p>is<\/p>\n<p>~r: For every real number x, either x \u2264 0 or x \u2265 1.<\/p>\n<p><strong>5. Check whether the following pair of statements is a negation of each other. Give reasons for your answer.<\/strong><\/p>\n<p><strong>(i) a + b = b + a is true for every real number a and b.<br \/>(ii) There exist real numbers a and b for which a + b = b + a.<\/strong><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>The negation of the statement:<\/p>\n<p>p: a + b = b + a is a true for every real number a and b.<\/p>\n<p>is<\/p>\n<p>~p: There exist real numbers are \u2018a\u2019 and \u2018b\u2019 for which a+b \u2260 b+a.<\/p>\n<p>So, the given statement is not the negation of the first statement.<\/p>\n<p>We have provided complete details of RD Sharma Solutions Class 11 Maths Chapter 31 Exercise 31.2. 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-class-11-solutions-chapter-31-exercise-312\"><\/span>FAQs on RD Sharma Class 11 Solutions Chapter 31 Exercise 31.2<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n<div id=\"rank-math-faq\" class=\"rank-math-block\">\n<div class=\"rank-math-list \">\n<div id=\"faq-question-1630397548552\" 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-312\"><\/span>How many questions are there in RD Sharma Solutions Class 11 Maths Chapter 31 Exercise 31.2?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>There are a total of 5 questions in RD Sharma Solutions Class 11 Maths Chapter 31 Exercise 31.2.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1630397633968\" 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-312-free-pdf\"><\/span>Where can I download RD Sharma Solutions Class 11 Maths Chapter 31 Exercise 31.2 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 31.2 free PDF from the above article.<\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1630397634734\" 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-312\"><\/span>What are the benefits of using Kopykitab\u2019s RD Sharma Solutions Class 11 Maths Chapter 31 Exercise 31.2?<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 31.2:<br \/>1. Correct answers according to the last CBSE guidelines and syllabus.<br \/>2. The solutions are 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 31.2:\u00a0In this exercise, we&#8217;ll look at the concept of negation in relation to a statement. The solutions are created by Kopykitab&#8217;s experts who have extensive experience in the field of education. The primary goal of providing RD Sharma Class 11 Solutions is to assist students, regardless &#8230; <a title=\"RD Sharma Class 11 Solutions Chapter 31 Exercise 31.2 (Updated for 2021-22)\" class=\"read-more\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-11-maths-chapter-31-exercise-31-2\/\" aria-label=\"More on RD Sharma Class 11 Solutions Chapter 31 Exercise 31.2 (Updated for 2021-22)\">Read more<\/a><\/p>\n","protected":false},"author":238,"featured_media":121606,"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\/68107"}],"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=68107"}],"version-history":[{"count":4,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/68107\/revisions"}],"predecessor-version":[{"id":121701,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/68107\/revisions\/121701"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media\/121606"}],"wp:attachment":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media?parent=68107"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/categories?post=68107"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/tags?post=68107"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}