I was given the following problem:
Let $V_1, V_2, \dots$ be an infinite sequence of Boolean variables. For each natural number $n$, define a proposition $F_n$ according to the following rules:
$\begin{align*} F_0 &= \text{False}\\ F_n &= (F_{n-1} \ne V_n)\;. \end{align*}$
Use induction to prove that for all $n$, $F_n$ is $\text{True}$ if and only if an odd number of the variables $V_k \;( k \le n)$ are $\text{True}$.
Can anyone help me out with at least beginning this problem? I'm not even entirely sure what it is asking.