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台大◆電機◆離散數學(B)題庫 下載題庫

109 年 - 109 國立臺灣大學_碩士班招生考試_電機工程研究所丙組:離散數學(B)#105860 

選擇:0題,非選:11題 我要補題 回報試卷錯誤
【非選題】
1.1. (15 points) Let S be a set of n elements. Let A, B be two different subsets of S chosen uniformly al Tandom. What is the probability that A is a subset of B? Show your derivation.

【非選題】
2.

2. (10 points) Solve the following recurrence (show your derivation):
  61e67b5490b87.jpg



【非選題】
3.

3. (15 points) Find a positive integer p such that 61e67b81b6b0e.jpg  or show that such an integer does not exist. Prove the correctness of your answer. (a) 61e67ba6e7df7.jpg



【非選題】
4.

(b) In propositional logic, 61e67bd2b0725.jpg is a functionally complete set.



【非選題】
5.

(c) If A and B are two countably infinite sets, then |A| = |B|.



【非選題】
6.(d) If S is an infinite set, then 2S must be uncountable.

【非選題】
7.(e) If a relation R is transitive, then R2 must also be transitive.

【非選題】
8.

(f) The set 61e67c2789ade.jpg is a partial ordering on the set of all positive functions f: N→  R+.



【非選題】
9.(g) If R1and R2 are two different relations defined on set A, then the (directed) graphs repre- senting R1 and R2 must not be isomorhpic.

【非選題】
10.5.(10 points) Let G = (V, E) be a simple planar undirected graph with every vertex ha 5. Is it true that G must have at least 12 vertices? Prove your answer.

【非選題】
11.6. (15 points) If a graph G has chromatic number k, but every graph G' resulting from removing one cdge from G has chromatic number at most k–1. Is it always true that every vertex in G has degree at least k–1? Prove your answer. Recall that the chromatic number of a graph is the minimum number of colors required to color all vertices such that adjacent vertices have different colors.

懸賞詳解

國二理化下第二次

題組:每題2.5分 羅素兄弟為了拍攝復仇者聯盟,打算利用下列溶液製作無限寶石,調皮的小勞勃·道尼和克里斯·漢斯沃卻偷偷拿來玩。  【題組】39....

50 x

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109 年 - 109 國立臺灣大學_碩士班招生考試_電機工程研究所丙組:離散數學(B)#105860-阿摩線上測驗

109 年 - 109 國立臺灣大學_碩士班招生考試_電機工程研究所丙組:離散數學(B)#105860