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(A deterrent is something that discourages a given activity.)
Prisons are usually considered a deterrent to crime.
The US maintains a fleet of missile submarines as part of its nuclear deterrent.
Yes, "deterrent" is the correct spelling.
A deterrent is something used to keep someone/something away. For example, mosquito repellent is a deterrent for mosquitos.
The mosquito flew away because of the insect deterrent.
The theft deterrent system will not work.