{"id":52726,"date":"2023-11-03T15:17:26","date_gmt":"2023-11-03T09:47:26","guid":{"rendered":"https:\/\/ccssmathanswers.com\/?p=52726"},"modified":"2023-11-10T12:28:13","modified_gmt":"2023-11-10T06:58:13","slug":"cardinal-number-of-a-set","status":"publish","type":"post","link":"https:\/\/bigideasmathanswers.com\/cardinal-number-of-a-set\/","title":{"rendered":"Cardinal Number of a Set Definition, Examples | How to find the Cardinal Number of a Set?"},"content":{"rendered":"<p>Cardinal Numbers are Numbers that are used for counting something. They are also called the Cardinals. Cardinals are meant by how many of anything is existing in a group. In other words, cardinal numbers are a collection of ordinal numbers. Learn about the Cardinal Number of a Set Definition, Solved Examples explained in detail in the further modules.<\/p>\n<h2>Cardinal Number of a Set &#8211; Definition<\/h2>\n<p>The Number of Distinct Elements present in a finite set is called the Cardinal Number of a Set. Usually, we define the size of a set using cardinality. The Cardinal Number of a Set A is denoted as n(A) where A is any set and n(A) represents the number of members in Set A.<\/p>\n<p>Consider a set of even numbers less than 15.<\/p>\n<p>Set A = {2, 4, 6, 8, 10, 12, 14}<\/p>\n<p>As Set A has 7 elements, the Cardinal Number of the Set is n(A) = 7<\/p>\n<p>Note:<\/p>\n<p>(i) Cardinal number of an infinite set is not defined.<\/p>\n<p>(ii) Cardinal number of the empty set is 0 since it has no element.<\/p>\n<p>Also, Check:<\/p>\n<ul>\n<li><a href=\"https:\/\/ccssmathanswers.com\/different-notations-in-sets\/\">Different Notations in Sets<\/a><\/li>\n<li><a href=\"https:\/\/ccssmathanswers.com\/subset\/\">Subset<\/a><\/li>\n<li><a href=\"https:\/\/ccssmathanswers.com\/intersection-of-sets\/\">Intersection of Sets<\/a><\/li>\n<\/ul>\n<h3>How to find the Cardinal Number of a Set?<\/h3>\n<p>1. Find the cardinal number of the following set<\/p>\n<p>E = { x : x &lt; 0, x \u2208 N }<\/p>\n<p>Solution:<\/p>\n<p>x&lt;0 means negative integers and they don&#8217;t fall under Natural Numbers.<\/p>\n<p>Therefore, the above set will not have any elements<\/p>\n<p>Cardinal Number of Set E is n(E) =0<\/p>\n<p>2. Find the Cardinal Number of the Following Set<\/p>\n<p>Q = { x : &#8211; 4 \u2264 x \u2264 3, x \u2208 Z }<\/p>\n<p>Solution:<\/p>\n<p>Given Q = { x : &#8211; 4 \u2264 x \u2264 3, x \u2208 Z }<\/p>\n<p>x={-4, -3, -2, -1, 0, 1, 2, 3 }<\/p>\n<p>Number of Elements in the above set is 8<\/p>\n<p>Therefore, Cardinal Number of Set Q is n(Q) = 8<\/p>\n<p>3. Find the Cardinal Number of the Set<\/p>\n<p>A = { x : x is even prime number }<\/p>\n<p>Solution:<\/p>\n<p>Among all the prime numbers 2 is the only even prime number and the set has only one element<\/p>\n<p>A ={2}<\/p>\n<p>Cardinal Number of a Set n(A) = 1<\/p>\n<p>4. Set D = {3, 4, 4, 5, 6, 7, 8, 8, 9}<\/p>\n<p>Solution:<\/p>\n<p>We know the cardinal number of a set is nothing but the number of distinct elements in the set<\/p>\n<p>Cardinal Number of Set D is n(D) = 7<\/p>\n<p>5. Find the Cardinal Number of a Set X = {letters in the word APPLE}<\/p>\n<p>Solution:<\/p>\n<p>Set X = {letters in the word APPLE}<\/p>\n<p>We know the cardinal number of a set is nothing but the number of distinct elements in the set<\/p>\n<p>x = {A, P, L, E}<\/p>\n<p>Cardinal Number of Set n(X) = 4<\/p>\n<p>6. Find the Cardinal Number of a Set<\/p>\n<p>P = {x | x \u2208 N and x<sup>2<\/sup> &lt;25}<\/p>\n<p>Solution:<\/p>\n<p>Given P = {x | x \u2208 N and x<sup>2<\/sup> &lt;25}<\/p>\n<p>Then P = {1, 2, 3, 4}<\/p>\n<p>Cardinal Number of Set P is 4 and is denoted by n(P) = 4<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Cardinal Numbers are Numbers that are used for counting something. They are also called the Cardinals. Cardinals are meant by how many of anything is existing in a group. In other words, cardinal numbers are a collection of ordinal numbers. Learn about the Cardinal Number of a Set Definition, Solved Examples explained in detail in &#8230; <a title=\"Cardinal Number of a Set Definition, Examples | How to find the Cardinal Number of a Set?\" class=\"read-more\" href=\"https:\/\/bigideasmathanswers.com\/cardinal-number-of-a-set\/\" aria-label=\"More on Cardinal Number of a Set Definition, Examples | How to find the Cardinal Number of a Set?\">Read more<\/a><\/p>\n","protected":false},"author":3,"featured_media":52965,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[5],"tags":[],"jetpack_featured_media_url":"https:\/\/bigideasmathanswers.com\/wp-content\/uploads\/2021\/02\/Cardinal-Number-of-a-Set.png","_links":{"self":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/52726"}],"collection":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/comments?post=52726"}],"version-history":[{"count":1,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/52726\/revisions"}],"predecessor-version":[{"id":92494,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/posts\/52726\/revisions\/92494"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media\/52965"}],"wp:attachment":[{"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/media?parent=52726"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/categories?post=52726"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bigideasmathanswers.com\/wp-json\/wp\/v2\/tags?post=52726"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}