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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
> 申論題
題組內容
1. (30%) John wants to choose his password for his new email account. How many different passwords are possible if a password is required to consist of
(e) 6 digits (0 to 9) of which the sum is 9, for example, 321103 or 110044?
相關申論題
(f) 6 digits (0 to 9) of which the sum is 20, for example, 326702 or 117344?
#436212
2. (10%) Show that is always true.
#436213
a) All students go to school.John is a studentTherefore John goes to school.
#436214
(b) All citizens pay their taxes. Tom pays his taxes. Therefore Tom is a citizen.
#436215
(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.
#436216
4. (10%) Use the Principle of Mathematical Induction to prove that
#436217
5. (10%) If , show that the number of assignments to assign n people into n-2 groups without group labeling is .
#436218
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.
#436219
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.
#436220
(a) Show the Hasse diagram of R.
#436221
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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
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