The correct answer is D.
A vector field $E$ is called solenoidal if $\nabla \cdot E = 0$. This means that the divergence of $E$ is zero, which implies that there are no sources or sinks of the field. In other words, the total amount of electric field lines entering a closed surface is equal to the total amount of electric field lines leaving the surface.
A vector field $E$ is called irrotational if $\nabla \times E = 0$. This means that the curl of $E$ is zero, which implies that there are no vortices in the field. In other words, the electric field lines do not form any closed loops.
A vector field can be both solenoidal and irrotational, but it can also be neither. For example, the electric field of a point charge is both solenoidal and irrotational. However, the electric field of an infinite line charge is solenoidal but not irrotational.
The statement “If $\nabla \cdot E = 0$, $E$ is called irrotational” is not true because a vector field can be solenoidal without being irrotational. For example, the electric field of a point charge is solenoidal but not irrotational.