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)
PS: Operations
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- shovan85
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Please post the question under proper sections with options. This will help others as well. Thankshaidgmat 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)
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
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