{"id":154005,"date":"2023-08-02T11:05:51","date_gmt":"2023-08-02T05:35:51","guid":{"rendered":"https:\/\/www.gkseries.com\/blog\/?p=154005"},"modified":"2023-08-02T11:05:52","modified_gmt":"2023-08-02T05:35:52","slug":"let-%f0%9d%91%88-12-%f0%9d%91%9b-let-%f0%9d%90%b4-%f0%9d%91%a5-%f0%9d%91%8b%f0%9d%91%a5-%e2%88%88-%f0%9d%91%8b-%f0%9d%91%8b-%e2%8a%86-%f0%9d%91%88-consider-the-following-t","status":"publish","type":"post","link":"https:\/\/www.gkseries.com\/blog\/let-%f0%9d%91%88-12-%f0%9d%91%9b-let-%f0%9d%90%b4-%f0%9d%91%a5-%f0%9d%91%8b%f0%9d%91%a5-%e2%88%88-%f0%9d%91%8b-%f0%9d%91%8b-%e2%8a%86-%f0%9d%91%88-consider-the-following-t\/","title":{"rendered":"Let \ud835\udc48 = {1,2, \u2026 , \ud835\udc5b}. Let \ud835\udc34 = {(\ud835\udc65, \ud835\udc4b)|\ud835\udc65 \u2208 \ud835\udc4b, \ud835\udc4b \u2286 \ud835\udc48}. Consider the following two statements on |\ud835\udc34|"},"content":{"rendered":"\n<figure class=\"wp-block-table\"><table><tbody><tr><td>Q.<\/td><td colspan=\"2\">Let \ud835\udc48 = {1,2, \u2026 , \ud835\udc5b}. Let \ud835\udc34 = {(\ud835\udc65, \ud835\udc4b)|\ud835\udc65 \u2208 \ud835\udc4b, \ud835\udc4b \u2286 \ud835\udc48}. Consider the following two statements on |\ud835\udc34|. <br>I.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 |\ud835\udc34| = \ud835\udc5b2<sup>\ud835\udc5b\u22121<\/sup> <br>II.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 |\ud835\udc34| = \u2211<sup>\ud835\udc5b<\/sup>\ud835\udc58=1\u00a0\u00a0\u00a0\u00a0 \ud835\udc58(<sup>\ud835\udc5b<\/sup>) \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0  <br>Which of the above statements is\/are TRUE?<\/td><\/tr><tr><td>&nbsp;<\/td><td>(A) Only I<\/td><td>(B) Only II<\/td><\/tr><tr><td>&nbsp;<\/td><td>(C) Both I and II<\/td><td>(D) Neither I nor II<\/td><\/tr><\/tbody><\/table><figcaption class=\"wp-element-caption\">Ans: Both I and II<\/figcaption><\/figure>\n\n\n\n<p><\/p>\n\n\n\n<p>Given, A = {(x, X)\u2223 x\u2208X, X\u2286U }, where U = {1, 2, \u2026,n}.<\/p>\n\n\n\n<p>As we know that The number of k element subsets of a set U with n elements =&nbsp;<sup>n<\/sup>C<sub>k<\/sub>.<\/p>\n\n\n\n<p>The number of possible ordered pairs (x, X) where x \u2208 X is k\u22c5&nbsp;<sup>n<\/sup>C<sub>k<\/sub>&nbsp;for a given value of k from 1 to n. So total number of ordered pairs in A,<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Q. Let \ud835\udc48 = {1,2, \u2026 , \ud835\udc5b}. Let \ud835\udc34 = {(\ud835\udc65, \ud835\udc4b)|\ud835\udc65 \u2208 \ud835\udc4b, \ud835\udc4b \u2286 \ud835\udc48}. Consider the following two statements on |\ud835\udc34|. I.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 |\ud835\udc34| = \ud835\udc5b2\ud835\udc5b\u22121 II.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 |\ud835\udc34| = \u2211\ud835\udc5b\ud835\udc58=1\u00a0\u00a0\u00a0\u00a0 \ud835\udc58(\ud835\udc5b) \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Which of the above statements is\/are TRUE? &nbsp; (A) Only I (B) Only II &nbsp; (C) Both I and II [&hellip;]<\/p>\n","protected":false},"author":419,"featured_media":154006,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5141],"tags":[5140],"offerexpiration":[],"class_list":["post-154005","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\/154005","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=154005"}],"version-history":[{"count":1,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/154005\/revisions"}],"predecessor-version":[{"id":154007,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/posts\/154005\/revisions\/154007"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media\/154006"}],"wp:attachment":[{"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/media?parent=154005"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/categories?post=154005"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/tags?post=154005"},{"taxonomy":"offerexpiration","embeddable":true,"href":"https:\/\/www.gkseries.com\/blog\/wp-json\/wp\/v2\/offerexpiration?post=154005"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}