113年 - 113 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#144359

(a)\( \forall x \exists y P(x, y) \)

(b)\( \forall y \exists x P(x, y) \)

(c)\( \exists x \forall y P(x, y) \)

(d)

2. Given \(a_0 = 0, a_1 = 1,\) and

Solve the equation. (20%)

(a) a = 387; b = 28; (5%)

(b)a = -78; b = 15; (5%)

(a) What is the in-order traversal?(10%)

(b) What is the post-order traversal?(10%)

(a) What is the probability that a positive integer selected at random from the set of positive integers not exceeding 100 is divisible by either 3 or 5? (10 %)

(b) What is the probability that a positive integer selected at random from the set of positive integers not exceeding 1000 is NOT divisible by either 7 or 9? (10 %)

6. A cookie shop has 7 different kinds of cookies. How many different ways can 10 cookies be chosen? Assume that only the type of cookie, and not the individual cookies or the order in which they are chosen, matters. (10 %)