For a first-order reaction, the half-life is given by the formula $t_{1/2} = \frac{0.693}{k}$, which clearly shows that it is a constant and is independent of the initial concentration of the reactant $[A]_0$ . On the other hand, the half-life of a second-order reaction is given by $t_{1/2} = \frac{1}{k[A]_0}$, meaning it is inversely proportional to the initial concentration. The rate of both first-order ($r = k[A]$) and second-order ($r = k[A]^2$) reactions depends on the reactant concentration. Therefore, only the second statement is correct.