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

I. a*b= b*a

II. a*0= a

III. (a*b)*c= a*(b*c)

Please post the question under proper sections with options. This will help others as well. Thanks

As per the question all will be True I think.

I. a*b= b*a

a*b = a + b - ab
b*a = b + a - ab

TRUE

II. a*0= a

a*0 = a + 0 - a.0 = a

TRUE

III. (a*b)*c= a*(b*c)

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

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

TRUE