$(2)$ Let $L=\{R\}$ where $R$ is a unary relation symbol. Find a first$-$order sentence $$ in the language $L$ such that for any structure $M,$ we have $M|=,>,R^M$ is an equivalence relation on $|M|(3)$ Show that $\sqrt[\phantom{2}]{2}$ is definable in the language of the arithmetic

$\{$:$,0,{?}^{\text{'}},+,\}.$ In other words, find a formula $(x)$ in $L_A$ such that for any

rinR,

$R|==[r],$ iff $,r=\sqrt[\phantom{2}]{2}$

$(4)$ The following question is from Problem $17\mathrm{.}3$:

Let $L=\{<mi\; id="EditorElement\_4881909">\}</mi>$ where $$ is a unary relation symbol, where

$|N|=N$ and ninNnN$(x)EE{x}_{0}dotsEE{x}_{n-1}$dots