I also think from this we can deduce that $x \in X$ and $x \notin \bigcup_{\alpha \in I} A_\alpha$, but I'm not sure where to go from there. I published a review article in a journal that is not well known. What are the major properties of indexed unions and intersections? I am posting the solutions in the order that interests me, which means that the blog navigation menus for “next post” and “previous post” don’t correspond to the order of the exercises in the book. MathJax reference. It may takes up to 1-5 minutes before you received it.

x\in X\setminus\bigcup_{\alpha\in I} A_\alpha &\iff x\in X, x\notin A_\alpha \text{ for all $\alpha\in I$}\\ These are almost entirely set in the concrete setting of the real line and Euclidean spaces, although there is some material on abstract metric and topological spaces. Work fast with our official CLI. How is it possible that a