Let ( ^ * ) be a binary operation defined on ( R ) by ( a * b= a+b 4 a, b R ) then the operation ( * ) is O examsnet com)

Step-by-step solution

Given that, ( a * b= a+b 4 ) So, ( b * a= b+a 4 = a+b 4 ) Then ( a^ * =b^ * a ) Therefore, it is commutative Now, ( a *(b * c)=a * ( b+c 4 ) ) ( = a+ b+c 4 4 = 4 a+b+c 16 (1) ) and ( (a * b) * c= ( a+b 4 ) * c ) ( = a+b 4 -c 4 = a+b+4 c 16 (2) ) Since, ( a *(b * c) (a * b) * c ) Therefore, it is not associative.