{"id":57813,"date":"2021-10-11T01:51:32","date_gmt":"2021-10-11T01:51:32","guid":{"rendered":"https:\/\/papersspot.com\/blog\/2021\/10\/11\/set-theory-question\/"},"modified":"2021-10-11T01:51:32","modified_gmt":"2021-10-11T01:51:32","slug":"set-theory-question","status":"publish","type":"post","link":"https:\/\/papersspot.com\/blog\/2021\/10\/11\/set-theory-question\/","title":{"rendered":"Set Theory Question"},"content":{"rendered":"<p>(i) Write p as a product of disjoint cycles. (ii) Find pq and qp.(iii) Write p as a product of the transpositions (12), (13), (14), (15), (16). (iv) Determine if q is an even or odd permutation.(v) Write q as a product of 3-cycles. <br \/>Let G be a group.(i) Let w 2 G. Prove that the inverse of w is unique. (ii) Let x, y 2 G. Prove that (xy)1 = y1x1. <br \/>For each of the following sets, either prove that it forms a group under matrix multiplication, or explain why it is not a group. <\/p>\n","protected":false},"excerpt":{"rendered":"<p>(i) Write p as a product of disjoint cycles. (ii) Find pq and qp.(iii) Write p as a product of the transpositions (12), (13), (14), (15), (16). (iv) Determine if q is an even or odd permutation.(v) Write q as a product of 3-cycles. Let G be a group.(i) Let w 2 G. Prove that [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[12],"class_list":["post-57813","post","type-post","status-publish","format-standard","hentry","category-research-paper-writing","tag-religion-and-theology"],"_links":{"self":[{"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/posts\/57813","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/comments?post=57813"}],"version-history":[{"count":0,"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/posts\/57813\/revisions"}],"wp:attachment":[{"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/media?parent=57813"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/categories?post=57813"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/tags?post=57813"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}