Let \tau a stopping time w.r.t. the filtration (F_n)_{n\in{\mathbb{N}}}. The stopped \sigma-field F_\tau associated with \tau is defined to be

F_\tau:={\{A\in{F}:A\cap{\{\omega:\tau(\omega)=n\}  \in{F_n} \text{ for all }n\geq {0}}\}.

I know this definition is equivalent to

F_\tau:={\{A\in{F}:A\cap{\{\omega:\tau(\omega)\leq  {n}\}\in{F_n} \text{ for all }n\geq {0}}\}.

But is it the same as

F_\tau:={\{A\in{F}:A\cap{\{\omega:\tau(\omega)<n\}  \in{F_n} \text{ for all }n\geq {0}}\}?
I have a feeling the answer is no, but I don't know how to start disproving it. Any help is appreciated! Thanks!