Let $f:[2,4] \rightarrow \mathbb{R}$ be a differentiable function such that $\left(x \log _e x\right) f(x)+\left(\log _e x\right) f(x)+f(x) \geq 1, x \in[2,4]$ with $f(2)=\frac{1}{2}$ and $f(4)=\frac{1}{4}$. Consider the following two statements : (A): $f(x) \leq{ }_{-1} 1$, for all $x \in[2,4]$ (B): $f(x) \geq \frac{1}{8}$, for all $x \in[2,4]$ Then,