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Google Arduino relay and Google Arduino transistor
The PIR should be able to send a signal either high or low and the Arduino should be able to read that signal the Arduino should be able to Output a signal either high or low to turn the relay or transistor on and off that will turn the fan on or off
The IDE has some example programs if you look at button or switch there's the basis of how to see one thing and do another this is a very good beginners project