There are given following lines on plane:
- $A: x=0$
- $B: y=0$
- $C_{i}:y=a_{i}x+b_{i}$ for $1\le i \le n$ so that these lines intersect with first two lines ($x=0,y=0$) at non-negative coordinates.
Let $G(i)$ be the set of lattice points in area bounded by $A,B,C_{i}$
Calculate $|G(1)\cup...\cup G(n)|$.
First of all i know that there should be used an inclusion-exclusion principle, but apart of $|G(i)|$ the rest is hard to calculate. Should i use Pick's theorem? If so then how?