{"id":4632,"date":"2016-05-17T11:49:00","date_gmt":"2016-05-17T06:19:00","guid":{"rendered":"http:\/\/mycbseguide.com\/blog\/ncert-solutions-class-11-maths-exercise-14-4\/"},"modified":"2016-05-17T13:33:41","modified_gmt":"2016-05-17T08:03:41","slug":"ncert-solutions-class-11-maths-exercise-14-4","status":"publish","type":"post","link":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-11-maths-exercise-14-4\/","title":{"rendered":"NCERT Solutions class-11 Maths Exercise 14.4"},"content":{"rendered":"<p style=\"text-align: justify;\"><strong>Exercise 14.4<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>1. Rewrite the following statements with \u201cif-then\u201d in five different ways conveying the same meaning.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>If a natural number is off then its square is also odd.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. (i) <\/strong>A natural number is odd implies that its square is odd.<\/p>\n<p style=\"text-align: justify;\"><strong>(ii) <\/strong>A natural is odd only if its square is odd.<\/p>\n<p style=\"text-align: justify;\"><strong>(iii) <\/strong>For a natural number to be odd it is necessary that its square is odd.<\/p>\n<p style=\"text-align: justify;\"><strong>(iv) <\/strong>For the square of a natural number to be odd it is sufficient that the number is odd.<\/p>\n<p style=\"text-align: justify;\"><strong>(v) <\/strong>If the square of a natural number is not odd then the natural number is not odd.<\/p>\n<hr \/>\n<p style=\"text-align: justify;\"><strong>2. Write the contrapositive and converse of the following statements:<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(i) If <\/strong><img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch14\/Ex14.4\/image001.png\" \/><strong> is a prime number, then <\/strong><img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch14\/Ex14.4\/image001.png\" \/><strong> is odd.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) If the two lines are parallel, then they do not intersect in the same plane.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iii) Something is cold implies that is has low temperature.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iv) You cannot comprehend geometry if you do not know how to reason deductively.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(v) <\/strong><img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch14\/Ex14.4\/image001.png\" \/><strong> is an even number implies that <\/strong><img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch14\/Ex14.4\/image001.png\" \/><strong> is divisible by 4.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. (i) <\/strong>The contrapositive of given statement is: If <img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch14\/Ex14.4\/image001.png\" \/> is not odd then <img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch14\/Ex14.4\/image001.png\" \/> is not a prime number.<\/p>\n<p style=\"text-align: justify;\">The converse of the given statement is: If <img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch14\/Ex14.4\/image001.png\" \/> is an odd number then <img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch14\/Ex14.4\/image001.png\" \/> is a prime number.<\/p>\n<p style=\"text-align: justify;\"><strong>(ii) <\/strong>The contrapositive of given statement is: If two lines intersect in the same plane then they are not parallel.<\/p>\n<p style=\"text-align: justify;\">The converse of the given statement is: If the two lines do not intersect in the same plane they are parallel.<\/p>\n<p style=\"text-align: justify;\"><strong>(iii) <\/strong>The contrapositive of given statement is: If something does not have low temperature then it is not cold.<\/p>\n<p style=\"text-align: justify;\">The converse of the given statement is: If something has low temperature then it is cold.<\/p>\n<p style=\"text-align: justify;\"><strong>(iv) <\/strong>The contrapositive of given statement is: If you know to reason deductively then you can comprehend geometry.<\/p>\n<p style=\"text-align: justify;\">The converse of the given statement is: If you do not know to reason deductively then you cannot comprehend geometry.<\/p>\n<p style=\"text-align: justify;\"><strong>(v) <\/strong>The contrapositive of given statement is: If <img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch14\/Ex14.4\/image001.png\" \/> is not divisible by 4 then <img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch14\/Ex14.4\/image001.png\" \/> is not an even number.<\/p>\n<p style=\"text-align: justify;\">The converse of the given statement is: If <img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch14\/Ex14.4\/image001.png\" \/> is divisible by 4 then <img decoding=\"async\" style=\"height: 15px; width: 13px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch14\/Ex14.4\/image001.png\" \/> is an even number.<\/p>\n<hr \/>\n<p style=\"text-align: justify;\"><strong>3. Write each of the following statements in the form \u201cif-then\u201d:<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(i) You get a job implies that your credentials are good.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) The Banana tree will bloom if it stays warm for a month.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iii) A quadrilateral is a parallelogram, if its diagonals bisect each other.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iv) To get an A<sup>+<\/sup> in the class then you do all the exercises of the book.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. (i) <\/strong>If you get a job then you credentials are good.<\/p>\n<p style=\"text-align: justify;\"><strong>(ii) <\/strong>If it says warm for a month then the banana trees will bloom.<\/p>\n<p style=\"text-align: justify;\"><strong>(iii) <\/strong>If the diagonals of a quadrilateral bisect each other then it is a parallelogram.<\/p>\n<p style=\"text-align: justify;\"><strong>(iv) <\/strong>If you get <img decoding=\"async\" style=\"height: 20px; width: 23px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/11\/maths\/ch14\/Ex14.4\/image002.png\" \/> in the class then you do all the exercises in the book.<\/p>\n<hr \/>\n<p style=\"text-align: justify;\"><strong>4. Give statements in (a) and (b). Identify the statements given below as contrapositive or converse of each other:<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(a) If you live in Delhi, then you have winter clothes.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(i) If you do not have winter clothes, then you do not live in Delhi.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) If you have winter clothes, then you live in Delhi.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(b) If a quadrilateral is a parallelogram then its diagonals bisect each other.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(i) If the diagonals of a quadrilateral do not bisect each other then the quadrilateral is not a parallelogram.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) If the diagonals of a quadrilateral bisect each other then the quadrilateral is a parallelogram.<\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. (a)<\/strong> <strong>(i)<\/strong> Contrapositive <strong>(ii)<\/strong> Converse<\/p>\n<p style=\"text-align: justify;\"><strong>(b)<\/strong> <strong>(i)<\/strong> Contrapositive <strong>(ii)<\/strong> Converse<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Exercise 14.4 1. Rewrite the following statements with \u201cif-then\u201d in five different ways conveying the same meaning. If a natural number is off then its square is also odd. Ans. (i) A natural number is odd implies that its square is odd. (ii) A natural is odd only if its square is odd. (iii) For &#8230; <a title=\"NCERT Solutions class-11 Maths Exercise 14.4\" class=\"read-more\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-11-maths-exercise-14-4\/\" aria-label=\"More on NCERT Solutions class-11 Maths Exercise 14.4\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[47,281],"tags":[],"class_list":["post-4632","post","type-post","status-publish","format-standard","hentry","category-cbse-class-11","category-ncert-solutions"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.0 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>NCERT Solutions class-11 Maths Exercise 14.4 | myCBSEguide<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-11-maths-exercise-14-4\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"NCERT Solutions class-11 Maths Exercise 14.4 | myCBSEguide\" \/>\n<meta property=\"og:description\" content=\"Exercise 14.4 1. Rewrite the following statements with \u201cif-then\u201d in five different ways conveying the same meaning. If a natural number is off then its square is also odd. Ans. (i) A natural number is odd implies that its square is odd. (ii) A natural is odd only if its square is odd. (iii) For ... 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