{"id":154019,"date":"2023-08-02T11:52:11","date_gmt":"2023-08-02T06:22:11","guid":{"rendered":"https:\/\/www.gkseries.com\/blog\/?p=154019"},"modified":"2023-08-02T11:52:13","modified_gmt":"2023-08-02T06:22:13","slug":"let-%f0%9d%90%ba-be-an-arbitrary-group-consider-the-following-relations-on-%f0%9d%90%ba","status":"publish","type":"post","link":"https:\/\/www.gkseries.com\/blog\/let-%f0%9d%90%ba-be-an-arbitrary-group-consider-the-following-relations-on-%f0%9d%90%ba\/","title":{"rendered":"Let \ud835\udc3a be an arbitrary group. Consider the following relations on \ud835\udc3a"},"content":{"rendered":"\n<p>Q. Let \ud835\udc3a be an arbitrary group. Consider the following relations on \ud835\udc3a:<\/p>\n\n\n\n<p>\ud835\udc45<sub>1<\/sub>: \u2200\ud835\udc4e, \ud835\udc4f \u2208 \ud835\udc3a, \ud835\udc4e \ud835\udc45<sub>1<\/sub>\ud835\udc4f if and only if \u2203\ud835\udc54 \u2208 \ud835\udc3a such that \ud835\udc4e = \ud835\udc54<sup>\u22121<\/sup>\ud835\udc4f\ud835\udc54<\/p>\n\n\n\n<p>\ud835\udc45<sub>2<\/sub>: \u2200\ud835\udc4e, \ud835\udc4f \u2208 \ud835\udc3a, \ud835\udc4e \ud835\udc45<sub>2<\/sub>\ud835\udc4f if and only if \ud835\udc4e = \ud835\udc4f<sup>\u22121<\/sup><\/p>\n\n\n\n<p>Which of the above is\/are equivalence relation\/relations?<\/p>\n\n\n\n<p>(A) \ud835\udc45<sub>1<\/sub> and \ud835\udc45<sub>2<\/sub><\/p>\n\n\n\n<p>(B) \ud835\udc45<sub>1<\/sub> only<\/p>\n\n\n\n<p>(C) \ud835\udc45<sub>2<\/sub> only<\/p>\n\n\n\n<p>(D) Neither \ud835\udc45<sub>1<\/sub> nor \ud835\udc45<sub>2<\/sub><\/p>\n\n\n\n<p>Ans: \ud835\udc45<sub>1<\/sub> only<\/p>\n\n\n\n<p>Solution:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"477\" height=\"535\" src=\"https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/08\/Screenshot-483.png\" alt=\"\" class=\"wp-image-154020\" srcset=\"https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/08\/Screenshot-483.png 477w, https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/08\/Screenshot-483-267x300.png 267w\" sizes=\"(max-width: 477px) 100vw, 477px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Q. Let \ud835\udc3a be an arbitrary group. Consider the following relations on \ud835\udc3a: \ud835\udc451: \u2200\ud835\udc4e, \ud835\udc4f \u2208 \ud835\udc3a, \ud835\udc4e \ud835\udc451\ud835\udc4f if and only if \u2203\ud835\udc54 \u2208 \ud835\udc3a such that \ud835\udc4e = \ud835\udc54\u22121\ud835\udc4f\ud835\udc54 \ud835\udc452: \u2200\ud835\udc4e, \ud835\udc4f \u2208 \ud835\udc3a, \ud835\udc4e \ud835\udc452\ud835\udc4f if and only if \ud835\udc4e = \ud835\udc4f\u22121 Which of the above is\/are equivalence relation\/relations? (A) \ud835\udc451 [&hellip;]<\/p>\n","protected":false},"author":419,"featured_media":154021,"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-154019","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\/154019","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=154019"}],"version-history":[{"count":1,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/154019\/revisions"}],"predecessor-version":[{"id":154022,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/154019\/revisions\/154022"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media\/154021"}],"wp:attachment":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media?parent=154019"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/categories?post=154019"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/tags?post=154019"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}