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轉學考-離散數學
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104年 - 104 淡江大學 轉學考 離散數學#53526
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題組內容
4
(a) Find a recurrence relation for the number of bit strings of length n that contains two consecutive Os. (10%)
其他申論題
【已刪除】(a)
#196582
【已刪除】(b) Give a general formula to find
#196583
【已刪除】2. Prove that every integer whose square is a multiple of 3 must divide by 3; i.e., where x, k, and m are integers. (20%) (Hint: prove by contraposition is must easier.)
#196584
【已刪除】3. Find the solution to the following recurrence relation and initial condition:
#196585
(b) What are the initial conditions? (5%)
#196587
(c) How many bit strings of length ten contain two consecutive Os. Use the above recurrence relation in (a) and (b) to solve it. (5%)
#196588
5. Let f {x) = ax + b and g(x) = cx + d, where a, b, c, and d are constants. Determine necessary and sufficient conditions on the constants a ,b, c, and d so that/。g = g。/ (10%)
#196589
(a) Represent the relation Rby a matrix. (4%)
#196590
(b) Draw a directed graph to represent R. (4%)
#196591
(c) Show what properties are satisfied by R. (2%)
#196592
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