Im trying to derive $N(A\cup B\cup C)$ with the help of Venn Diagram.

$$|A\cup B\cup C| = |A| + |B| + |C| - |A\cap B| - |B\cap C| - |A\cap C| + |A\cap B\cap C|$$

I have reached the step where $N(A)+N(B)+N(C)$ is computed.I Can see the terms are getting cancelled out during addition of $N(A)+N(B)+N(C)$ how does this happen.

EDIT:

I don't know how to Type Symbols so im attaching a picture 

![enter image description here](https://i.stack.imgur.com/zx1b3.png)
![enter image description here](https://i.stack.imgur.com/BmiOh.png)

What i want to know is how N(A)+N(B)+N(C) is obtained after cancellation