问题 填空题

已知A={a,b,c},B={0,1,2},则满足条件f(a)+f(b)>f(c)的映射f:A→B有 ______个.

答案

f(a)=0,1,2;f(b)=0,1,2;f(c)=0,1,2.

当f(c)=0时,满足条件的映射有8个:f(c)=0,f(a)=0,f(b)=1;f(c)=0,f(a)=0,f(b)=2;f(c)=0,f(a)=1,f(b)=0;f(c)=0,f(a)=1,f(b)=1;f(c)=0,f(a)=1,f(b)=2;f(c)=0,f(a)=2,f(b)=0;f(c)=0,f(a)=2,f(b)=1;f(c)=0,f(a)=2,f(b)=2.

当f(c)=1时,满足条件的映射有6个:f(c)=1,f(a)=f(b)=1;f(c)=1,f(a)=2,f(b)=1;f(c)=1,f(a)=1,f(b)=2;f(c)=1,f(a)=2,f(b)=2;f(c)=1,f(a)=2,f(b)=0;f(c)=1,f(a)=0,f(b)=2.

当f(c)=2时,满足条件的映射有3个:f(c)=2,f(a)=1,f(b)=2;f(c)=2,f(a)=2,f(b)=1;f(c)=2,f(a)=2,f(b)=2.

综上所述,满足条件f(a)+f(b)>f(c)的映射f:A→B有17个.

故答案为:17.

填空题
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