Let E and V respectively denote the electric field and electric...

The electric field $E$ and electric potential $V$ are related by $E = -\dfrac{dV}{dr}$.

At the midpoint of the line joining two equal and opposite charges (an electric dipole), the net electric potential $V = 0$, but the net electric field $E \neq 0$. Thus, if $E \neq 0$, $V$ can be zero.

Inside a uniformly charged hollow spherical shell, the electric field $E = 0$ everywhere, but the electric potential $V$ is non-zero and constant (equal to the potential at the surface). Thus, if $V \neq 0$, $E$ can be zero.

Therefore, statements (1) and (4) are correct.