I have been presented with the follwing question and I want to see if the method I have used works. I have my doubts.
We recall that $M$ is an elementary extension of $N= \langle \mathbb{N}; +, ., 0, 1 \rangle$ if for a formula $\phi(x)$ and every element n of the naturals, $\phi(n)$ is true in $N$ if and only if it is true in $M$.
My thought process is then consider the formula $\exists x[0<x$ and $1<x]$ then the negation of this is true and so must be true in the extension as well?
Is this the right approach? If not, what am I missing?