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99年 - 99 淡江大學 轉學考 離散數學#55471
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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)
相關申論題
3. Prove or disprove: If (mod 4), where a and b are integers, then (mod 4). (12 pts)
#208749
4. Find the smallest equivalence relation on {1,2,3} that contains (1,2). (12 pts) Justify your answer.
#208750
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
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
(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
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%)
#211029
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
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