Final answer:
The system that includes the core, mantle, and crust of the Earth is the geosphere. These layers are part of the Earth's internal structure and are separate from the hydrosphere, atmosphere, and biosphere.
Step-by-step explanation:
The structures mentioned in the question, the core, mantle, and crust, are all part of the Earth's internal composition. The correct answer to what system includes these parts is the geosphere.
The geosphere is defined by the Earth's solid parts, which include the core (both the inner and outer core), the mantle, and the crust, both the continental and the oceanic crusts. The geosphere is distinct from the hydrosphere, which includes all the water on Earth; the atmosphere, which is the layer of gases surrounding the planet; and the biosphere, which encompasses all regions of the Earth where life exists.