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97年 - 97 淡江大學 轉學考 離散數學#55809
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5. Prove or disprove that any subset of size six from the set S= {1, 2, 3,..., 9} must contain two elements whose sum is 10. (20%)
相關申論題
1. Prove that if an integer a is such that a — 2 is divisible by 3, then α2- 1 is divisible by 3. (20%)
#211025
(b) and indicate what the answer is, do not evaluate it.
#213089
(c) Write a generating function corresponding to the problem in
#213088
(b) If God exists, tlien 1+1=3 or 2+2 = 4.
#213081
(a) If2+2 = 4, then 1+1 =3.
#213080
7. Use mathematical induction to prove that 3 divides n3+2n whenever n is a nonnegative integer. (15 pts) (3整除n3+2n, n為非負整數）（必須以歸納證明的方法證得）
#208753
6. Apply Dijkstra’s Algorithm to find a shortest path from a to f. Indicate what is your shortest path and the total weight of the path. You must show every step in order to get full credits. (14 pts)
#208752
5. How many nonnegative integer solutions are there to the equation x1 x2 + x3 + x4 = 21 such that (12 pts) Show enough work to get full credits.
#208751
4. Find the smallest equivalence relation on {1,2,3} that contains (1,2). (12 pts) Justify your answer.
#208750
3. Prove or disprove: If (mod 4), where a and b are integers, then (mod 4). (12 pts)
#208749
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