For each of the following collections of sets, define a set $A_n$ for each $n \in \mathbf{N}$ such that the indexed collection $\left\{A_n\right\}_{n \in \mathrm{N}}$ is precisely the given collection of sets. Then find both the union and intersection of the indexed collection of sets.
(a) $\{[1,2+1),[1,2+1 / 2),[1,2+1 / 3), \ldots\}$
(b) $\{(-1,2),(-3 / 2,4),(-5 / 3,6),(-7 / 4,8), \ldots\}$.