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104年 - 104 國立交通大學_碩士班考試入學試題_資訊聯招：線性代數與離散數學#113284
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題組內容
2. (a)(4 points) Give a recursive definition of the set S of odd integers.
(b) (5 points) Prove by induction that for all n
∈
Z, 2n + 1
∈
S, where Z is the set of integers.
相關申論題
(a) (3 points) A computer randomly prints three-digit codes, with no repeated digits in any code (for example, 387, 072, 760). What is the minimum number of codes that must be printed in order to guarantee that at least five of the codes are identical?
#484113
(b) (3 points) What is the largest value of n for which Kn (a complete graph on n vertices) is planar?
#484114
(c) (3 points) If the permutations of 1,2,3,4,5,6 are written in lexicographic order, with 123456 in position #1, 123465 in position #2, etc., find the permutation in position #484.
#484115
(a) (4 points) an, = the number of bit strings of length n with an even number of 0s. Describe the sequence recursively. Include initial condition and assume that the sequence begins with a1.
#484116
(b) (4 points) Find the number of ways in which nine identical blocks can be given to four children, if the oldest child gets at most three blocks.
#484117
(c) (4 points) Suppose A is a set with n symbols, IAI = n. Find the number of symmetric binary relations on A.
#484118
(d) (4 points) How many non-isomorphic simple undirected graphs with 5 vertices and 3 edges?
#484119
(a) (2 points) Which statements are always false?
#484120
(b) (2 points) Which statements are al ways true?
#484121
(c) (2 points) Which statements are equivalent to the statement (B)?
#484122
相關試卷
104年 - 104 國立交通大學_碩士班考試入學試題_資訊聯招：線性代數與離散數學#113284
104年 · #113284
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