I'm not sure if this is the right place to ask but what does the coproduct symbol signify? I came across it in a book and just found out what it's called, but that's as far as I've gotten.
As with most symbols, it depends on context. It can mean the category-theoretic coproduct, which is defined in terms of a universal property. Or it can mean "disjoint union", where the elements from each of the sets are "tagged" with the set they came from, so that even if an element belongs to two of the sets, that element will show up as two different elements in the disjoint union.
If you tell us which book you found it in, and the name of the chapter, we can probably be more helpful.