{"id":199719,"date":"2025-03-12T11:16:50","date_gmt":"2025-03-12T11:16:50","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=199719"},"modified":"2025-03-12T11:16:54","modified_gmt":"2025-03-12T11:16:54","slug":"write-the-set-of-points-from-4-to-2-but-excluding-3-and-2-as-a-union-of-intervals","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/03\/12\/write-the-set-of-points-from-4-to-2-but-excluding-3-and-2-as-a-union-of-intervals\/","title":{"rendered":"Write the set of points from -4 to -2 but excluding -3 and -2 as a union of intervals"},"content":{"rendered":"\n

Write the set of points from -4 to -2 but excluding -3 and -2 as a union of intervals<\/p>\n\n\n\n

The correct answer and explanation is :<\/strong><\/mark><\/p>\n\n\n\n

The given set of points is from \u22124-4 to \u22122-2, but we are excluding \u22123-3 and \u22122-2. To express this set as a union of intervals, we need to break it into parts where the excluded points create gaps.<\/p>\n\n\n\n

    \n
  1. The original interval before exclusions: [\u22124,\u22122][-4, -2]<\/li>\n\n\n\n
  2. Excluding \u22123-3 means breaking the interval into two parts: [\u22124,\u22123)\u222a(\u22123,\u22122][-4, -3) \\cup (-3, -2]<\/li>\n\n\n\n
  3. Excluding \u22122-2 further means removing it from (\u22123,\u22122](-3, -2], leaving just (\u22123,\u22122)(-3, -2) instead.<\/li>\n<\/ol>\n\n\n\n

    Thus, the correct union of intervals representation is: [\u22124,\u22123)\u222a(\u22123,\u22122)[-4, -3) \\cup (-3, -2)<\/p>\n\n\n\n

    \n\n\n\n

    Explanation (300 words)<\/strong><\/h3>\n\n\n\n

    To correctly express a set of numbers as a union of intervals, we need to determine the continuous sections of the set and use interval notation appropriately. Intervals come in four main types:<\/p>\n\n\n\n

      \n
    • Closed interval<\/strong> [a,b][a, b] includes both endpoints aa and bb.<\/li>\n\n\n\n
    • Open interval<\/strong> (a,b)(a, b) excludes both endpoints.<\/li>\n\n\n\n
    • Half-open (or half-closed) intervals<\/strong> [a,b)[a, b) or (a,b](a, b] include one endpoint but not the other.<\/li>\n<\/ul>\n\n\n\n

      For our given problem, the set of points is initially from \u22124-4 to \u22122-2, meaning the complete closed interval is [\u22124,\u22122][-4, -2]. However, we must exclude the points \u22123-3 and \u22122-2, which introduces breaks in the interval.<\/p>\n\n\n\n

        \n
      • Step 1: Exclude \u22123-3<\/strong>
        Removing \u22123-3 means splitting the interval [\u22124,\u22122][-4, -2] into two parts: [\u22124,\u22123)[-4, -3) and (\u22123,\u22122](-3, -2]. The notation [\u22124,\u22123)[-4, -3) means \u22124-4 is included, but \u22123-3 is not.<\/li>\n\n\n\n
      • Step 2: Exclude \u22122-2<\/strong>
        Since \u22122-2 was included in the second interval (\u22123,\u22122](-3, -2], removing it turns that into (\u22123,\u22122)(-3, -2).<\/li>\n<\/ul>\n\n\n\n

        Now, the final expression is: [\u22124,\u22123)\u222a(\u22123,\u22122)[-4, -3) \\cup (-3, -2)<\/p>\n\n\n\n

        This means we include all numbers from \u22124-4 to just before \u22123-3, and from just after \u22123-3 up to just before \u22122-2, effectively excluding \u22123-3 and \u22122-2.<\/p>\n","protected":false},"excerpt":{"rendered":"

        Write the set of points from -4 to -2 but excluding -3 and -2 as a union of intervals The correct answer and explanation is : The given set of points is from \u22124-4 to \u22122-2, but we are excluding \u22123-3 and \u22122-2. To express this set as a union of intervals, we need to […]<\/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-199719","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/199719","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=199719"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/199719\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=199719"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=199719"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=199719"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}