KCET2014MathematicsDifferentiation
For any two real numbers, an operation ( * ) defined by ( a * b=1+a b ) is
Options
- Acommutative but not associative
- Bassociative but not commutative
- Cneither commutative nor associative
- Dboth commutative and associative
Correct answer
A. commutative but not associative
Step-by-step solution
Given that, a * b=1+a b (1) Now, b * a=1+b a=1+a b=a * b a * b=b^ * a Thus, ^ * is commutative. Now, (a * b) * c=(1+a b) * c=1+(1+a b) c=1+c+a b c But, a *(b * c)=a *(1+b c)=1+a(1+b c)=1+a+a b c So, (a * b) * c a *(b * c) Thus, ^ * is not associative. Hence, ^ * is commutative but not associative.