∈ belongs to. N∈Z means that n is an integer. N∈R means that n belongs to a real number.

∪ yes and, A∪B means meeting the meaning of a or B.

∩ is the intersection, and A∩B means satisfying a and B.

∑ is an accumulation symbol.

M={x|x=3m+5n, m, n∈Z} is the format of the set. The former refers to the set of what, here is X, and the latter meets the condition of X.