Let $U,W\subseteq V$, vector subspaces then:

1) $U\subseteq W\phantom{\rule{thickmathspace}{0ex}}\u27f9\phantom{\rule{thickmathspace}{0ex}}{W}^{\perp}\subseteq {U}^{\perp}$

2) $(U+W{)}^{\perp}={U}^{\perp}\cap {W}^{\perp}$

1) $U\subseteq W\phantom{\rule{thickmathspace}{0ex}}\u27f9\phantom{\rule{thickmathspace}{0ex}}{W}^{\perp}\subseteq {U}^{\perp}$

2) $(U+W{)}^{\perp}={U}^{\perp}\cap {W}^{\perp}$