If the operation ~$\circledast$~ is defined for all integers a and b by a~$\circledast$~b =a + b - ab which of the following statements must be true for all integers a, b, and c ?

I. ~$a\circledast b=b\circledast a$~

II. ~$a\circledast 0=a$~

III. ~$\left ( a\circledast b \right )\circledast c=a\circledast \left ( b\circledast c \right )$~