105年 - 105 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#146286

1. Let A={1, 2, 3, 4} , B={2, 3, 4, 5}, and C ={3, 4, 5, 6} FindA – B, B – C, A – (B – C) and (A - B) – C.(10%)

2. Let A={1, 2, 3}. Find all one-to-one (and therefore onto)function f: A A. (10%)

3. Evaluate the following sum: S = .(10%)

4. How many three-element subsets are three of the five-element set{1, 2, 3, 4, 5}？(10%)

5. The Yreka Bakery sells only four kinds of cookies; chocolatechip, oatmeal, peanut butter, and raisin. How many differentcombinations of eight cookies can we buy？(10%)

6. Show that the graph in the following figure has noHamiltonian path.(20%)

(1)Is relation R antisymmetric？(5%)

(2)Is relation R irreflexive？(5%)

(3)Is relation R transitive？(5%)

(1)

(2)

(3)