[理工] [離散]97台大電機

看板Grad-ProbAsk作者 (好崩潰)時間14年前 (2011/11/17 00:03), 編輯推噓1(106)
留言7則, 4人參與, 最新討論串1/1
目如下: 第一題 Let V be the set of vertices of a digraph D, and for u,v屬於 V, defined (u,v)屬於 R if u=v or there exists a path from u to v.Is R equivalence relation? 答案是NO 為什麼?? 我覺得三個條件都符合耶~~ -------------------------------------------------------------------------------- 第二題 Let R be the relation defined on NxN (N為自然數) as follows:((m,n),(p,q))屬於R iff m≡p mod 3 or n≡q mod 5. Which of the following is false? (1)R is equivalence relation. (2)R is reflexive. (3)R is symmetric. (4)R is not transitive. (5)None of the above. 答案是(1) 可是我覺得R應該不符合symmetric... 所以應該是(1)(3) -------------------------------------------------------------------------------- 以上 有勞高手解答 鋼溫!! -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 223.138.240.24

11/17 00:17, , 1F
第一題應該是因為有向圖 某點u 有到v的path 但v到u不一定
11/17 00:17, 1F

11/17 00:18, , 2F
有path 所以不滿足symmetric
11/17 00:18, 2F

11/17 01:19, , 3F
第二題: (7,0)R(4,0) 然後7=4mod3 => 4=7mod3 => (4,0)R(7,0
11/17 01:19, 3F

11/17 21:08, , 4F
((m,p),(n,q))其中不管是m,n三同餘的話還是p,q五同餘的話
11/17 21:08, 4F

11/17 21:09, , 5F
你變成((n,q),(m,p))還是一樣會有n,m三同餘或是p,q五同餘
11/17 21:09, 5F

11/17 21:10, , 6F
所以符合對稱性沒錯啊
11/17 21:10, 6F

11/17 22:45, , 7F
我後來找例子做了...對是符合的...感謝各位的解答
11/17 22:45, 7F
文章代碼(AID): #1EmzxPSK (Grad-ProbAsk)