Vector Calculus

If a vector field $\vec{V}$ is irrotational everywhere in a simply connected domain, which of the following is necessarily true?

Options:

• (A) \nabla \times \vec{V} = \vec{0} \text{ and } \vec{V} = \nabla \phi
• (B) \nabla \cdot \vec{V} = 0
• (C) \nabla \times \vec{V} \ne \vec{0}
• (D) \vec{V} \text{ is solenoidal}