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108年 - 108 國立中山大學_碩士班招生考試_資工系(資安)：離散數學與演算法#105778
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題組內容
1. A committee of 14 is to be selected from 10 men and 10 women. In how many ways can the selectio be carried out if
(b) there must be at least eight men?
其他申論題
7.(a) Find the coefficient of.
#450333
(b) Find the coefficient offor .
#450334
8.Let with . Prove that if and , then .
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(a) there must be seven men and seven women?
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2. Verify that , for primitive statements , and .
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(a) Wiite a quantified statement to express the proper subset relation .
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(b) Negate the result in part (a) to determine when .
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4. (a) Consider an chessboard. It contains eighty-one squares and one square. How many squares?
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(b) Now consider an chessboard for some fixed . ForI , how many squares are contained in this chessboard?
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5. Let be a set of five positive integers the maximum of which is at most 9. Prove that the sums of the elements in all the nonempty subsets of S cannot all be distinct.
#450343
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