I see you've uploaded an image with a few geometric problems. Let me walk through the problems and explain how to approach them.

Problem Breakdown:

1. First Problem: This asks which set of three line segments cannot form a triangle. For this, you apply the triangle inequality theorem, which states that the sum of any two sides must be greater than the third side.

2. Second Problem: You're given triangle ABC with $AB = 1 \, \text{cm}$ and $BC = 4 \, \text{cm}$, and you're asked to find possible values for $AC$ when it's an integer. Again, the triangle inequality principle applies here.

3. Third Problem: For triangle ABC, with $AB = 2 \, \text{cm}$ and $BC = 7 \, \text{cm}$, you're tasked with finding the length of side $AC$, where it is a natural number. Again, the triangle inequality will help narrow down the possible values for $AC$.

4. Fourth Problem: You need to prove an inequality related to the sides of triangle ABC, given specific side lengths.

Would you like me to explain the steps to solve any specific question or help with a detailed solution for any of them?