{"id":154123,"date":"2023-08-02T14:48:25","date_gmt":"2023-08-02T09:18:25","guid":{"rendered":"https:\/\/www.gkseries.com\/blog\/?p=154123"},"modified":"2023-08-02T14:48:27","modified_gmt":"2023-08-02T09:18:27","slug":"consider-the-first-order-predicate-formula-%f0%9d%9c%91-%e2%88%80%f0%9d%91%a5-%e2%88%80%f0%9d%91%a7-%f0%9d%91%a7%f0%9d%91%a5-%e2%87%92-%f0%9d%91%a7-%f0%9d%91%a5-%e2%88%a8-%f0%9d%91%a7-1","status":"publish","type":"post","link":"https:\/\/www.gkseries.com\/blog\/consider-the-first-order-predicate-formula-%f0%9d%9c%91-%e2%88%80%f0%9d%91%a5-%e2%88%80%f0%9d%91%a7-%f0%9d%91%a7%f0%9d%91%a5-%e2%87%92-%f0%9d%91%a7-%f0%9d%91%a5-%e2%88%a8-%f0%9d%91%a7-1\/","title":{"rendered":"Consider the first order predicate formula \ud835\udf11 \u2200\ud835\udc65 [(\u2200\ud835\udc67 \ud835\udc67|\ud835\udc65 \u21d2 ((\ud835\udc67 = \ud835\udc65) \u2228 (\ud835\udc67 = 1))) \u21d2"},"content":{"rendered":"\n<figure class=\"wp-block-table\"><table><tbody><tr><td colspan=\"4\">Q. Consider the first order predicate formula \ud835\udf11:<br> \u2200\ud835\udc65 [(\u2200\ud835\udc67 \ud835\udc67|\ud835\udc65 \u21d2 ((\ud835\udc67 = \ud835\udc65) \u2228 (\ud835\udc67 = 1))) \u21d2 \u2203\ud835\udc64 (\ud835\udc64 > \ud835\udc65) \ud835\udda0 (\u2200\ud835\udc67 \ud835\udc67|\ud835\udc64 \u21d2 ((\ud835\udc64 = \ud835\udc67) \u2228 (\ud835\udc67 = 1)))] <br>Here \u2018\ud835\udc4e|\ud835\udc4f\u2019 denotes that \u2018\ud835\udc4e divides \ud835\udc4f\u2019, where \ud835\udc4e and \ud835\udc4f are integers. Consider the following sets: <br>S1.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 {1,2,3, \u2026 , 100} <br>S2.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Set of all positive integers <br>S3.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Set of all integers <br>Which of the above sets satisfy \ud835\udf11?<\/td><\/tr><tr><td>(A) S1 and S2<\/td><td>(B) S1 and S3<\/td><td>(C) S2 and S3<\/td><td>(D) S1, S2 and S3<\/td><\/tr><\/tbody><\/table><figcaption class=\"wp-element-caption\">Ans: (C) S2 and S3<\/figcaption><\/figure>\n\n\n\n<p><\/p>\n\n\n\n<p>Solution:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"453\" height=\"551\" src=\"https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/08\/Screenshot-488.png\" alt=\"\" class=\"wp-image-154124\" srcset=\"https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/08\/Screenshot-488.png 453w, https:\/\/www.gkseries.com\/blog\/wp-content\/uploads\/2023\/08\/Screenshot-488-247x300.png 247w\" sizes=\"(max-width: 453px) 100vw, 453px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Q. Consider the first order predicate formula \ud835\udf11: \u2200\ud835\udc65 [(\u2200\ud835\udc67 \ud835\udc67|\ud835\udc65 \u21d2 ((\ud835\udc67 = \ud835\udc65) \u2228 (\ud835\udc67 = 1))) \u21d2 \u2203\ud835\udc64 (\ud835\udc64 > \ud835\udc65) \ud835\udda0 (\u2200\ud835\udc67 \ud835\udc67|\ud835\udc64 \u21d2 ((\ud835\udc64 = \ud835\udc67) \u2228 (\ud835\udc67 = 1)))] Here \u2018\ud835\udc4e|\ud835\udc4f\u2019 denotes that \u2018\ud835\udc4e divides \ud835\udc4f\u2019, where \ud835\udc4e and \ud835\udc4f are integers. Consider the following sets: S1.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 {1,2,3, \u2026 [&hellip;]<\/p>\n","protected":false},"author":419,"featured_media":154125,"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-154123","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\/154123","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=154123"}],"version-history":[{"count":1,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/154123\/revisions"}],"predecessor-version":[{"id":154126,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/154123\/revisions\/154126"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media\/154125"}],"wp:attachment":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media?parent=154123"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/categories?post=154123"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/tags?post=154123"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}