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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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2. Verify that
, for primitive statements
, and
.
其他申論題
(b) Find the coefficient offor .
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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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(b) there must be at least eight men?
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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.
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6. (a) Fermat's Theorem. If is a prime, prove that for each .
#450344
, for primitive
statements 
, and 
.
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, for primitive
statements , and .