Are the following statements true or false?

1. if f⃗ is a vector field in 3-dimensional space satisfying div(f⃗ )=1, and s is a closed surface oriented outward, then ∬sf⃗ ⋅da⃗ is equal to the volume enclosed by s.

2. if f⃗ is a vector field in 3-dimensional space, and w is a solid region with boundary surface s, then ∬s f⃗ ⋅da⃗ =∭wdiv(f⃗ )dv.

3. if ∬sf⃗ ⋅da⃗ =12 and s is a flat disk of area 4π, then div(f⃗ )=3/π.

4. if f⃗ is a vector field in 3-dimensional space, then grad(div(f⃗ ))=0⃗ .

5. if f⃗ and g⃗ are vector fields satisfying div(f⃗ )=div(g⃗ ), then f⃗ =g⃗ .