Measurability — functions relative to a coarse $\sigma$-field

Let $\Omega=\{1,2,3,\dots,10\}$, $A=\{1,2\}$ and $\mathbf F=\{\phi,A,A^C,\Omega\}$, consider the following functions: $X(w)=100 \forall w\in\Omega$; $Y(w)=100$ if $w\in A$, $400$ if $w\notin A$; $Z(w)=w \forall w\in\Omega$. Then which of the following is true?