Convergence of the maximum and minimum sequences

Let $\{a_n\}_{n\ge1}$ and $\{b_n\}_{n\ge1}$ be two convergent sequences of real numbers. For $n\ge1$, define $u_n=\max\{a_n,b_n\}$ and $v_n=\min\{a_n,b_n\}$. Then