I started to get excited about mathematical analysis. So I bought a mathematical analysis book and started to study. But because of the reason that, book do not have solutions I do not have an idea where to start and how to prove the following:
Let $A_t$, $t \in T$, be a family of sets, and let $X$ be a set. Prove the identities:
$$X \setminus \bigcup A_t = \bigcap (X\setminus A_t)$$
$$X \setminus \bigcap A_t = \bigcup(X\setminus A_t) $$
Could you please help me? Also I need a book recommendation about mathematical analysis which goes like a theorem and its proof, a theorem and its proof.. Do you have any suggestions?