$(4)$ We fix a first$-$order language L$.$ Let $L=\{c,f,R\}$ where $c$ is a constant symbol, $f$ be a unary $(1-$place$)$

function and $R$ be a binary $(2-$place$)$ relation. Define a model $M=$

$($:$|M|,c^M,f^M,R^M$:$)$ by:

$|M|=\{a,b,k\}$

$c^M=a$

$f^M(a)=b,f^M(b)=a,f^M(k)=a$

$R^M=\{(a,a),(a,b),(b,a),(b,b)\}$

Explain whether or not

$M|==$AAx$(f(x)-=cR(x,c))$