Let $\mathcal{L}=\{P\}$ where $P$ is a unary relation symnbol and let $\mathcal{M}$ a finite $\mathcal{L}$-structure. Show that there exists $\sigma \in Sent_{\mathcal{L}}$ such that for all $\mathcal{L}$-structures $\mathcal{N}$, we have
$$\mathcal{N} \vDash \sigma \text{ if and only if } \mathcal{M} \cong \mathcal{N}$$
I am having issues with this problem, I have tried to prove it by supposing the oposite and reaching a contradiction, also I have tried to prove it directly with some possible sentences, but I don't get it. Possible ideas would be appreciated.