{"id":244999,"date":"2025-07-05T15:10:23","date_gmt":"2025-07-05T15:10:23","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=244999"},"modified":"2025-07-05T15:10:26","modified_gmt":"2025-07-05T15:10:26","slug":"find","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/05\/find\/","title":{"rendered":"Find \u200b"},"content":{"rendered":"\n

Find \u200b(a) the number of subsets and \u200b(b) the number of proper subsets of the set. The set of days of the week. .<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

Let’s break down the problem step by step for the set of days of the week, which is represented as:S={Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday}S = \\{ \\text{Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday} \\}S={Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday}<\/p>\n\n\n\n

(a) Number of subsets:<\/h3>\n\n\n\n

The number of subsets of a set is given by the formula:Number of subsets=2n\\text{Number of subsets} = 2^nNumber of subsets=2n<\/p>\n\n\n\n

where nnn is the number of elements in the set. In this case, there are 7 elements (the 7 days of the week), so n=7n = 7n=7.Number of subsets=27=128\\text{Number of subsets} = 2^7 = 128Number of subsets=27=128<\/p>\n\n\n\n

This means there are 128 subsets<\/strong> of the set of days of the week, including the empty set and the set itself.<\/p>\n\n\n\n

(b) Number of proper subsets:<\/h3>\n\n\n\n

A proper subset is a subset that is not identical to the original set. The formula for the number of proper subsets is:Number of proper subsets=2n\u22121\\text{Number of proper subsets} = 2^n – 1Number of proper subsets=2n\u22121<\/p>\n\n\n\n

This is because we exclude the set itself from the total number of subsets. Using n=7n = 7n=7 again:Number of proper subsets=27\u22121=128\u22121=127\\text{Number of proper subsets} = 2^7 – 1 = 128 – 1 = 127Number of proper subsets=27\u22121=128\u22121=127<\/p>\n\n\n\n

Therefore, there are 127 proper subsets<\/strong> of the set of days of the week.<\/p>\n\n\n\n

Explanation:<\/h3>\n\n\n\n
    \n
  • Subsets<\/strong>: A subset of a set is any collection of elements from the set, including the empty set (which contains no elements) and the set itself. For a set with nnn elements, there are 2n2^n2n possible subsets because each element can either be included or excluded in a subset.<\/li>\n\n\n\n
  • Proper subsets<\/strong>: A proper subset is any subset that does not equal the original set. Since the set of all subsets (which includes the set itself) has 2n2^n2n subsets, we subtract one to exclude the set itself, leaving 2n\u221212^n – 12n\u22121 proper subsets.<\/li>\n<\/ul>\n\n\n\n

    So, the answers are:<\/p>\n\n\n\n

      \n
    • (a) The number of subsets is 128<\/strong>.<\/li>\n\n\n\n
    • (b) The number of proper subsets is 127<\/strong>.<\/li>\n<\/ul>\n\n\n\n
      \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

      Find \u200b(a) the number of subsets and \u200b(b) the number of proper subsets of the set. The set of days of the week. . The Correct Answer and Explanation is: Let’s break down the problem step by step for the set of days of the week, which is represented as:S={Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday}S = \\{ \\text{Monday, Tuesday, Wednesday, […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-244999","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/244999","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=244999"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/244999\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=244999"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=244999"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=244999"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}