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108年 - 108 國立中山大學_碩士班招生考試_資工系(甲組)：離散數學#105776
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6. Given a nonempty language
, prove that if
, then
.
其他申論題
(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 . For , how manyke 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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7.(a) Find the coefficient of.
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(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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2. Verify that , for primitive statements , and .
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, prove that if
, then
.
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, prove that if, then.