Let X be normed space, and U and V its subspaces such that: $\displaystyle U \cap V = \{0\}$

Let $\displaystyle \{x_n\} \subset U$ $\displaystyle \{y_n\} \subset V$ be the sequences such that:

$\displaystyle x_n + y_n \rightarrow 0$

Is it true, that: $\displaystyle x_n \rightarrow 0$ and $\displaystyle y_n \rightarrow 0$ ?