what is defined subset?

Answer 1

I've never heard of a "defined" subset. If you have a set of numbers (they could be integers, or real, or complex, but we'll stick with integers just to make it obvious), than a "defined" subset just means that you know (can "define") a selection from that set. For example, given a set...

{6, 27, 3, 6, 11, 32}

... a defined subset can be simply {27, 11}.

There's no magic here and it's not a special term (in fact, everyone just calls that a subset I'm pretty sure you're just a tad confused because your professor/author of your textbook is using this term for no apparent reason). This question is in geometry however, so I'll take it a bit further (using simple geometry).

If you know a set is a region within the square of width times height, you can say that a defined sub-set of the are of the square is the lower-right triangle portion, which would be width times height divided by two (again, super simple example of a potentially area subset... not trying to offend).

If, however, you're talking about a "proper subset", that's something different entirely and I would erase this answer in an instant to explain.

Basically, your question is unclear.