请教一道PREP上的数学（已经解决了）

If the operation * is defined for all integers a and b by a*b=a+b-ab, which of the following statements must be ture for all integers a, b and c?

I  a*b=b*a

II  a*0=a

III  (a*b)*c=a*(b*c)

a. I only

b. II only

c. I & II only

d. I & III only

e. I, II and III

谢谢帮忙解答了~~~

a*b=a+b-ab

(a*b)*c=a*(b*c)

左边=(a+b-ab)*c=a+b-ab+c-(a+b-ab)c=a+b-ab+c-ac-bc+abc

右边=a*(b+c-bc)=a+(b+c-bc)-a(b+c-bc)=a+b+c-bc-ab-ac+abc

左边等于右边，所以III也是对的，选E

这类题就是替换，括号内的先运算

谢谢LS了~~~很清楚~~