{"id":160299,"date":"2023-09-25T15:33:51","date_gmt":"2023-09-25T10:03:51","guid":{"rendered":"https:\/\/www.gkseries.com\/blog\/?p=160299"},"modified":"2023-09-25T15:33:52","modified_gmt":"2023-09-25T10:03:52","slug":"let-n-be-the-set-of-natural-numbers-consider-the-following-sets","status":"publish","type":"post","link":"https:\/\/www.gkseries.com\/blog\/let-n-be-the-set-of-natural-numbers-consider-the-following-sets\/","title":{"rendered":"Let N be the set of natural numbers. Consider the following sets"},"content":{"rendered":"\n<p>Q. Let <em>N <\/em>be the set of natural numbers. Consider the following sets.<\/p>\n\n\n\n<p><em>P<\/em>: Set of Rational numbers (positive and negative)<\/p>\n\n\n\n<p><em>Q<\/em>: Set of functions from {0, 1} to <em>N R<\/em>: Set of functions from <em>N <\/em>to {0, 1} <em>S<\/em>: Set of finite subsets of <em>N<\/em>.<\/p>\n\n\n\n<p>Which of the sets above are countable?<\/p>\n\n\n\n<p>(A) <em>Q <\/em>and <em>S <\/em>only\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (B) <em>P <\/em>and <em>S <\/em>only\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (C) <em>P <\/em>and <em>R <\/em>only\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (D) <em>P<\/em>, <em>Q <\/em>and <em>S <\/em>only<\/p>\n\n\n\n<p>Ans: <em>P<\/em>, <em>Q <\/em>and <em>S <\/em>only<\/p>\n\n\n\n<p>Sol:<\/p>\n\n\n\n<p>Set of functions from {0, 1} to N are\u00a0<em>countable<\/em>\u00a0because it has one to one correspondence to N.<\/p>\n\n\n\n<p>Set of functions from N to {0, 1} is\u00a0<em>uncountable<\/em>, because it has one to one correspondence to set of real numbers between (0 and 1).<\/p>\n\n\n\n<p>Set of finite subsets of N is\u00a0<em>countable<\/em>.<\/p>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Q. Let N be the set of natural numbers. Consider the following sets. P: Set of Rational numbers (positive and negative) Q: Set of functions from {0, 1} to N R: Set of functions from N to {0, 1} S: Set of finite subsets of N. Which of the sets above are countable? (A) Q [&hellip;]<\/p>\n","protected":false},"author":419,"featured_media":160300,"comment_status":"open","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-4)","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-4)","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-4)","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":[5141],"tags":[5140],"class_list":["post-160299","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-gate","tag-gate-questions"],"_links":{"self":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/160299","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/users\/419"}],"replies":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/comments?post=160299"}],"version-history":[{"count":1,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/160299\/revisions"}],"predecessor-version":[{"id":160301,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/160299\/revisions\/160301"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media\/160300"}],"wp:attachment":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media?parent=160299"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/categories?post=160299"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/tags?post=160299"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}