The correct statement is: The mantle is both solid and liquid while the inner core is entirely solid.
To elaborate, the Earth's mantle is primarily solid rock, but it can behave as a viscous fluid over geological time scales, which allows for the convection currents that drive plate tectonics. The inner core, on the other hand, is solid, made primarily of iron and nickel, despite the extremely high temperatures that would normally cause these materials to be in a liquid state.