离散数学考试

满足。a * b = a + b - 3，b * a = b +a - 3；∵ a + b - 3 = b + a - 3，∴a * b = b * a，满足交换律；c * ( a * b )，将c看作原式的 "a"，( a * b )看作原式的 "b"，则c * ( a * b ) =c +( a * b ) - 3 = c + (a + b - 3 ) - 3 = a + b + c - 6；同样，b * ( a * c ) = b + ( a * c ) - 3 = b + ( a + c - 3 ) - 3 = a + b + c - 6；两式右边相等，所以左边相等，即c * ( a * b ) =b * ( a * c )，满足结合律 。