104年 - 104 淡江大學轉學考離散數學#53526

科目：轉學考-離散數學 | 年份：104年 | 選擇題數：0 | 申論題數：11

試卷資訊

所屬科目：轉學考-離散數學

選擇題 (0)

申論題 (11)

【已刪除】(a)

【已刪除】(b) Give a general formula to find

【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.)

【已刪除】3. Find the solution to the following recurrence relation and initial condition:

(a) Find a recurrence relation for the number of bit strings of length n that contains two consecutive Os. (10%)

(b) What are the initial conditions? (5%)

(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%)

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%)

(a) Represent the relation Rby a matrix. (4%)

(b) Draw a directed graph to represent R. (4%)

(c) Show what properties are satisfied by R. (2%)