[理工] [離散]97台大電機

[jim055006 (好崩潰)]

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~~

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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)

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以上
有勞高手解答
鋼溫!!                  

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→ feabries: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
→ feabries:有path 所以不滿足symmetric
→ yraid:第二題: (7,0)R(4,0) 然後7=4mod3 => 4=7mod3 => (4,0)R(7,0
推 kiwidoit:((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
→ kiwidoit: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
→ kiwidoit:所以符合對稱性沒錯啊
→ jim055006:我後來找例子做了...對是符合的...感謝各位的解答