## bvb

Please, help find out the truth or falsity of this:
Let $(X_i)_{i\in J}$ -family of subsets in V,V - an inner product space. $X_i\perp X_j, \quad X_i+X_i^\perp=V \quad \forall i$, and let $X=\overline{sp\bigcup X_i}$. Can we say that $X+X^\perp=V$?