Consider the family of sets An=(0,1+1n]A_n = \left(0, 1 + \frac{1}{n}\right]An=(0,1+n1] for n∈Nn \in \mathbb{N}n∈N and Bm=[1−1m,2)B_m = \left[1 - \frac{1}{m}, 2\right)Bm=[1−m1,2) for m∈Nm \in \mathbb{N}m∈N. Determine the set (⋂n=1∞An)∪(⋃m=1∞Bm)\left(\bigcap_{n=1}^{\infty} A_n\right) \cup \left(\bigcup_{m=1}^{\infty} B_m\right)(⋂n=1∞An)∪(⋃m=1∞Bm).
[0,2)[0, 2)[0,2)
(0,2)(0, 2)(0,2)
[0,2][0, 2][0,2]
(0,2](0, 2](0,2]