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 ?