Hi,

so here is my problem:

Given $\displaystyle F_{1},...,F_{n}, n \ge 2 $ subspaces of $\displaystyle X$ and if $\displaystyle F=F_{1} \Delta F_{2} \Delta ... \Delta F_n$,( where $\displaystyle A \Delta B:= (A-B)\cup (B-A)=(A \cup B) \cap (A^{c} \cup B^{c})$ (the symmetric difference)), show that

$\displaystyle x \in F \Leftrightarrow |\{i \in N|x \in F\}|$ is an uneven number. ( where $\displaystyle |\{ ...\}|= $ the number of items in a set).

I tried something with the indicator function but it didn't lead to anything.

Sorry for the bad english.

Thanks in advance!!!