114年 - 114 國立嘉義大學_碩士班招生考試試題_資訊工程學系：離散數學#144123

(a) If the value of p → q is false, determine the value of ( p ∨ q) → q . (10%)

(b) If the value of p → q is true, can you determine the value of p ∨ ( p ↔ q) ? (10%)

二、The following graph represents the communication channels and their respective time delays (in minutes) between eight communication centers. The centers are depicted as vertices, the channels as edges, and the communication time delay for each channel is indicated by the weight of the edge. Suppose communication center a broadcasts news through all its channels at 8:00 a.m. Other centers will rebroadcast the news through their channels immediately upon receiving it. For communication centers b, c, d, e, f, g, and h, determine the earliest time each receives the news. (20%)

三、There are 36 distinct time slots available for scheduling classes at a university. Given that there are 698 classes, determine the minimum number of classrooms required. (10%)

(a) You wish to pick an even number of black cards and an odd number of red cards? (10%)

(b) You wish to pick at least two of each symbol, but no more than 5 hearts and 6 spades? (10%)

(a) What is the probability that a randomly chosen person who tests positive for the disease actually has the disease? (10%)

(b) What is the probability that a randomly chosen person who tests negative for the disease does not indeed have the disease? (10%)

六、Solve the recurrence relation a_n-6a_n-1-7a_n-2 =0 for n≧5 where a₃ = 344 and a₄ = 2400. (10%)