= Solution
\b[True]. Choose a <basis> $u_1,\ldots,u_r$ of $U$ and extend it to a <basis> $u_1,\ldots,u_r,w_1,\ldots,w_s$ of the finite-dimensional <vector space> $V$. Put $W=\operatorname{span}(w_1,\ldots,w_s)$. Every <basis> vector belongs to $U+W$, so $U+W=V$. <Linear independence> of the complete <basis> makes a vector belonging to both spans necessarily zero. Therefore
$$
\boxed{U\cap W=\{0\},\qquad V=U\oplus W}.
$$
This constructs a <direct-sum complement>; it need not be unique.
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