CUET Preparation Today
Consider the binary oeration * : R × R → R defined as a*b = a + b / 2 |
* is commutative and associative * is neither commutative nor associative * is commutative but not associative * is associative but not commutative |
* is commutative but not associative |
$a*b=\frac{a+b}{2}$, so $b*a=\frac{a+b}{2}$ → commulative $(a*b)*c=\frac{\frac{a+b}{2}+c}{2}$ $a*(b*c)=\frac{a+\frac{b+c}{2}}{2}$ $=\frac{a+b+2c}{4}=\frac{2a+b+c}{4}$ → not associative as $(a*b)*c≠a*(b*c)$ |
