Are the following statements true or false?

? True False  1. If $\vec{F}$ is a vector field in 3-dimensional space satisfying $\mathrm{div}(\vec{F}) = 1$, and $S$ is a closed surface oriented outward, then $\displaystyle \iint\limits_S \vec{F} \cdot d\vec{A}$ is equal to the volume enclosed by $S.$

? True False  2. If $\vec{F}$ and $\vec{G}$ are vector fields satisfying $\mathrm{div}(\vec{F}) = \mathrm{div}(\vec{G})$, then $\vec{F} = \vec{G}.$

? True False  3. If $\displaystyle \iint\limits_S \vec{F} \cdot d \vec{A} = 12$ and $S$ is a flat disk of area $4\pi$, then $\mathrm{div}(\vec{F}) = 3 / \pi$.

? True False  4. If $\vec{F}$ is a vector field in 3-dimensional space, then $\mathrm{grad}( \mathrm{div} (\vec{F})) = \vec{0}.$

? True False  5. If $\vec{F}$ is a vector field in 3-dimensional space, and $W$ is a solid region with boundary surface $S$, then $\displaystyle \iint\limits_S \vec{F} \cdot d\vec{A} = \iiint\limits_W \mathrm{div}(\vec{F}) \, dV .$