109年 - 109 國立高雄大學_碩士班招生考試_資訊工程學系：離散數學#103285

科目：研究所、轉學考(插大)◆離散數學 | 年份：109年 | 選擇題數：0 | 申論題數：17

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所屬科目：研究所、轉學考(插大)◆離散數學

選擇題 (0)

申論題 (17)

(a) 6 digits (0 to 9)

(b) 6 distinct digits (0 to 9) , for example, 521467 or 216098?

(c) 6 strictly increasing digits (0 to 9), for example, 014679 or 134689?

(d) 6 increasing digits (0 to 9), for example, 011467 or 111344?

(e) 6 digits (0 to 9) of which the sum is 9, for example, 321103 or 110044?

(f) 6 digits (0 to 9) of which the sum is 20, for example, 326702 or 117344?

2. (10%) Show that is always true.

a) All students go to school.
John is a student
Therefore John goes to school.

(b) All citizens pay their taxes.
Tom pays his taxes.
Therefore Tom is a citizen.

(c) All people who are concerned about the environment recycle their plastic containers. Margarita is not concerned about the environment. Therefore Margarita does not recycle her plastic containers.

4. (10%) Use the Principle of Mathematical Induction to prove that

5. (10%) If , show that the number of assignments to assign n people into n-2 groups without group labeling is .

6. (10%) S = {1, 2, 3, 4, 5, 6, 7, 8, 9}. If six elements are selected from S, show that two of them must have the sum 10.

7. (8%) Consider the students of a class. Let R is the relation that x R y if x and y live in a same hometown. Determine whether R is reflexive, symmetric, antisymmetric, or transitive.

(a) Show the Hasse diagram of R.

(b) What are the (i) maximal, (ii) minimal, (iii) greatest, and (iv) least elements of the poset (S, R)?

(c) B={2, 3}. What are the (i) lower and (ii) upper bounds of B?