How are sets written, and what are empty and domain sets?

"As with most of math, it turns out to be useful to define symbols for these concepts, because then we can talk about them more precisely and concisely. We normally list the members of a set using curly braces, like this: A = { Dad , Lizzy } or B = { Lizzy , T.J. , Marina } Note that it doesn’t matter what order you list the members in. The set F of females contains Mom, Lizzy, and Marina but it’s not like Mom is the “first” female or anything. That doesn’t even make any sense. There is no “first.” A set’s members are all equally members. So P is the same whether we write it like this: P = { Dad , Mom } or this: P = { Mom , Dad } . Those are just two different ways of writing the same thing. The set E that had nobody in it can be written like this, of course: E = { } but we sometimes use this special symbol instead: E = ∅ . However you write it, this kind of set (one that has no elements) is referred to as an empty set. The set H, above, contained all the members of the group under consideration. Sometimes we’ll refer to “the group under consideration” as the “domain of discourse.” It too is a set, and we usually use the symbol Ω to refer to it. So in this case, Ω = { Mom , Marina , T.J. , Dad , Lizzy } . Some authors use the symbol U for this, and call it the “universal set.”"