Final answer:
For a fire to ignite and continue burning, fuel and air (which contains oxygen) are necessary components from the choices provided. Water is not needed for combustion, and earth is not a direct element of the fire triangle.
Step-by-step explanation:
A fire requires three essential components to ignite and continue burning: fuel, a heat source, and oxygen. Among the options provided, a) Fuel and c) Air are necessary for a fire to ignite and sustain itself. Fuel serves as the combustible material that the fire consumes, and air, which contains about 21 percent oxygen, is critical as most fires need at least 16 percent oxygen to burn. Water, mentioned in the given options, is actually used to extinguish fires, not sustain them, and earth, while a significant component in the ecology of soils, is not directly involved in the combustion process that allows a fire to burn.
Soils do contain elements like earth, air, water, and the living organisms (biological 'fire') that interact with these components, but they are not directly related to the fire triangle, which specifically includes only oxygen, fuel, and a heat source.