设集合M={-1,0,1},N={2,3,4,5,6},映射f:M→N,使对任意x∈M,都有x+f(x)+xf(x)是奇数,求这样的映射f的个数!
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![设集合M={-1,0,1},N={2,3,4,5,6},映射f:M→N,使对任意x∈M,都有x+f(x)+xf(x)是奇数,求这样的映射f的个数!](/uploads/image/z/13088362-58-2.jpg?t=%E8%AE%BE%E9%9B%86%E5%90%88M%3D%7B-1%2C0%2C1%7D%2CN%3D%7B2%2C3%2C4%2C5%2C6%7D%2C%E6%98%A0%E5%B0%84f%3AM%E2%86%92N%2C%E4%BD%BF%E5%AF%B9%E4%BB%BB%E6%84%8Fx%E2%88%88M%2C%E9%83%BD%E6%9C%89x%2Bf%EF%BC%88x%EF%BC%89%2Bxf%EF%BC%88x%EF%BC%89%E6%98%AF%E5%A5%87%E6%95%B0%2C%E6%B1%82%E8%BF%99%E6%A0%B7%E7%9A%84%E6%98%A0%E5%B0%84f%E7%9A%84%E4%B8%AA%E6%95%B0%21)
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设集合M={-1,0,1},N={2,3,4,5,6},映射f:M→N,使对任意x∈M,都有x+f(x)+xf(x)是奇数,求这样的映射f的个数!
设集合M={-1,0,1},N={2,3,4,5,6},映射f:M→N,使对任意x∈M,都有x+f(x)+xf(x)是奇数,求这样的映射f的个数!
设集合M={-1,0,1},N={2,3,4,5,6},映射f:M→N,使对任意x∈M,都有x+f(x)+xf(x)是奇数,求这样的映射f的个数!
x,f(x)不能同时为偶数,排除0到2,4,6的映射
总共的映射数为5^3-(5^2)*3=50个