[kanji]

5.Let $U$ be a subspace of a vector space $V$. For each $v\in V$, define
$v+U:=\left\{\,\right. v+u\left|\,\right. u\in U\left.\,\right\}$ .
5.1) Under what conditions is $v+U$ a subspace of $V$ ?.
The set $v+U$ is called an affine subspace of $V$.
5.2) Show that any two affine subspace of the form $v+u$ and $w+U$ are either equal or disjoint.