Measurability between two explicit finite $\sigma$-fields

Let $\Omega=\{1,2,3,4\}$. Consider the two $\sigma$-fields $\mathbf F_1=\{\phi,\Omega,\{1\},\{2\},\{1,2\},\{3,4\},\{2,3,4\}, \{1,3,4\}\}$ and $\mathbf F_2=\{\phi,\Omega,\{1,2\},\{3,4\}\}$. Let $f$ denote a function from $(\Omega,\mathbf F_1)$ to $(\Omega,\mathbf F_2)$. Then: