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I have two questions regarding the proof of inclusion and exclusion principle (IEP or PIE), and the proof is based on the usage of characteristic functions. I have attached both the proof and my questions in the image file. Any help is much appreciated and thanks in advance.

I have two questions regarding the proof of inclusion and exclusion principle (IEP or PIE), and the proof is based on the usage of characteristic functions.
 
I have attached both the proof and my questions in the image file.
 
Any help is much appreciated and thanks in advance.
 

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