Fundamental Concepts

I am trying something I have seen on many blogs around the internet: I will work through all the exercises in Munkres’ textbook, Topology. I have never tried anything like this before and it will definitely test my ability to stay motivated as I tend to get bored easily. So, without further ado, I present the exercises of Topology, Chapter 1, “Set Theory and Logic”, Section 1, “Fundamental Concepts”.

  1. Check the distributive laws for $\cup$ and $\cap$ and DeMorgan’s laws.

This amounts to showing the following are true:

$A \cap (B \cup C) = \{ x \mid x \in A \mbox{ and } x \in (B \cup C) \}$