# Convergence on normed spaces

Let X be normed space, and U and V its subspaces such that: $U \cap V = \{0\}$
Let $\{x_n\} \subset U$ $\{y_n\} \subset V$ be the sequences such that:
$x_n + y_n \rightarrow 0$
Is it true, that: $x_n \rightarrow 0$ and $y_n \rightarrow 0$ ?