Set theory seems to pop up in many different fields of mathematics. As someone with a CS degree, I've only encountered very basic set theory; dealing with non-specific sets, and their intersections, unions, and complements. Furthermore, this turned out to be useful in logic and probability which are central in a CS degree.
I was wondering, what are the motivating factors for learning set theory on a deeper level? Where is it useful, and do you have any good examples of real life problems (I assume they will be vocational problems, and not personal life problems) that can be solved using set theory?
EDIT: It has been correctly pointed out that this is a duplicate. The suggested duplicate simply didn't show up in my searches.