[理工] [離散] 關係

[ceo890710 (Drinking)]

98台大資工- Tru or False

(d) The Hasse diagram for a total ordering is a chain

(e) It is possible that there are multiple topological orders for
    a partially ordered set

想問這兩個選項..

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98中山資工

Let R be the relation on A={1,2,3,4,5,6,7},where the directed graph

associated with R consists of the two components,each a directed cycle

,shown below.Find all integers n's such that 1<n<30 and R^n = R

1 → 2        5
↑　↓      ↗ ↘
4 ← 3　　 7 ←　6

這題解答部分是寫 R^(12k) 不太懂這個地方..
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97清大資工

Let S be the set of all strings of English letters.consider the

following relations on S and determine whether

(a)R1 = {(a,b)|a and b have no letters in common} is reflexive or not

我想問這個選項..no letters in common是指什麼樣的字..

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97政大資科

Let A be the set of all bit strings of length 11. Define an equivalence

relation R on A with the condition that xRy iff bits x and y have the same

number of 1's.Then
(b)The quotient set A/R has ____ equivalence classes

我想問其中A/R是代表什麼..




不好意思問題有點多..希望高手能給小弟我一些指教 謝謝:)



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◆ From: 1.169.173.40
※ 編輯: ceo890710       來自: 1.169.173.40         (08/07 21:25)
※ 編輯: ceo890710       來自: 1.169.173.40         (08/07 21:26)
推 mqazz1:台大資工那兩題應該都是true
※ 編輯: ceo890710       來自: 1.169.173.40         (08/07 21:33)
→ ceo890710:(d)我剛查過瞭解了~我想問(e)是為什麼呢..
推 mqazz1:97台大資工的(e)因為topological sort不一定唯一
→ mqazz1:97清大資工 照題意 不具reflexive
→ metalalive:97清大, no letter in common --> a,b中沒有任何一個字
→ metalalive:元相同