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112年 - 112 教育部公費留學考試試題：離散數學#125724
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題組內容
5. (24%) Let A={1,2,3,4} and B={x,y,z}.
A. (3%) List three functions from A to B.
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(二)若簡支梁兩端有側向支撐，不計該構件自重，試求該梁能承受之最大均佈載重為何？(單位：kgf/cm)
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2. (10%) If three integers are selected, at random and without replacement, from {1,2,3,...,99,100}, what is the probability such that their sum is even ?
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3. (10%) For three sets A,B, and C, please simplify the following set expression
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4. (15%) For what base do we find that 251+445=1026.
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B. (3%) How many functions f: A→B are there?
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C. (3%) How many functions f: A→B are one-to-one?
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D. (3%) How many functions g: B→A are there?
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E. (3%) How many functions g: B→A are one-to-one?
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F. (3%) How many functions f: A→B satisfy f(1)=x?
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G. (3%) How many functions f: A→B satisfy f(1)=f(2)=x?
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