(i) For all a , b ∊ N , a * b = $\frac{a+b}{2}$ Now , b * a = $\frac{b+a}{2}$ = $\frac{a+b}{2}$ = a * b Thus, the binary operation * is commutative. (ii) Let a , b , c ∊ N a * b * c = a * $\left(\frac{b+c}{2}\right)$ = $\frac{a+\frac{b+c}{2}}{2}$ = $\frac{2a+b+c}{4}$ a * b * c = $\left(\frac{a+b}{2}\right)$ * c = $\frac{\frac{a+b}{2}+c}{2}$ = $\frac{a+b+2c}{4}$ ∴ a * b * c ≠ a * b * c Thus, the binary operation * is not associative.