When I was in the digital logic class at school, the teacher taught me basic Boolean algebra rules and some common simplification methods and then assigned some homework, but when I went to prove it myself, I found that I couldn't solve it.
When I read the proofs of these questions：
I'm getting more confused. I think I know the basic rules of Boolean algebra, but I can't figure out why it works here. In addition to the basic rules of Boolean algebra, are there any other ways to solve this problem using Boolean algebra? I tried to search for methods on the Internet but they were all simple proofs. I could understand them but they did not help me understand the above two proof questions.