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Yes. Solid rocket fuel contains its own oxidizer.
A device that ignites the fuel & oxidizer mixture in the rocket engine when a "burn" is to begin.it lights the rocket.
A solid rocket engine uses a fuel and an oxidizer. The oxidizer when burned delivers oxygen to the fuel so that it can burn. Most rockets use oxidizers because when the rocket burns it uses so much oxygen that they need a readily available supply.
Chemical rocket
Chemical rocket
Hybrid rockets use a hybrid fuel-oxidizer system, usually a solid fuel with a liquid oxidizer. This allows simpler construction and higher reliability (like solid fuel rockets) but retains the ability to throttle the engine on demand or even turn it off and restart it (like liquid fuel rockets).
If its fuel has an oxidizer (oxygen-producing solid fuel) in it like solid rocket fuel, then yes.
A jet engine takes oxygen from the air to burn with its fuel. A rocket engine has to take oxygen or some comparable oxidizer with it.
Jet engines capture ambient oxygen to use as an oxidizer for their fuel. In a sense, an afterburner is somewhat like a rocket, but it still uses ambient oxygen for the oxidizer. Rockets are different. Since they are designed to travel out of the atmosphere, they must carry both their oxidizer and their fuel. Many hydrocarbons will work as a rocket fuel including petrol (gasoline), diesel, and even tar. But they must all also have oxygen as a second fuel for the oxidizer. Solid Rockets have both the oxidizer and fuel built into the same matrix, somewhat like gunpowder. The "Oxidizer" doesn't have to be oxygen, or even contain oxygen. Nitric Acid has been utilized as an oxidizer in some rocket engines.
As regards the main engines on the rocket, there is an ignitor associated with each rocket motor. An internal "blowtorch" of fuel and oxidizer in each engine is ignited with spark plugs.
Solid fuel
There are two main types of rockets: liquid-fuel and solid-fuel. Liquid-fuel rockets consist of a fuel and oxygen (or other oxidizer) in liquid state. They are combined in a combustion chamber and ignited. The fuel flow to the engine can be controlled, the amount of thrust produced can be regulated and the engine can be turned off or on as needed. Solid-fuel rockets consist of a fuel and oxidizer that are pre-mixed in a solid form. Once the solid fuel is ignited, the resulting thrust cannot be regulated or turned off. This fuel system is simpler, safer, and cheaper-but less efficient-than that of a liquid-fuel rocket.