Let F be any vector field of the form $\mathbf{F} = f \left( x \right) \mathbf{i} + g \left( y \right) \mathbf{j} + h \left( z \right) \mathbf{k}$ and let G be any vector field of the form $\mathbf{G} = f \left( y, z \right) \mathbf{i} + g \left( x, z \right) \mathbf{j} + h \left( x, y \right) \mathbf{k}$. Indicate whether the following statements are true or false by placing "T" or "F" to the left of the statement.

 1. F is incompressible
 2. F is irrotational
 3. G is incompressible
 4. G is irrotational