How does APT resolve dependencies?

Question

linux

Let's say package a is installed first, which depends on libraries a1 and a2. Then package b is installed, which depends on b1 and a1.
1. When package a is removed, library a1 will not be removed, right?
2. Removing package b will remove both a1 and b1?
3. Will the packages (by dependencies) that are included in the system kernel, such as sed, grep, be removed?

Answer 1

When uninstalling with apt-get, only the explicitly specified package is removed, its dependencies are not touched at all. Use apt-get autoremove to clean up time dependencies . Accordingly, the answers to your questions are: no, no, yes, only if you write apt-get remove core-utils.
Here you can read some tips on how to see dependencies, work with dpkg.