Since the Question is now deleted, I'll link to the timeline for your post.
The Question as most recently given begins with a splashy graphic, taken I assume from the Powerpoint presentation you mentioned. The title contains the phrase Rough Sets, but this is not defined or even mentioned elsewhere in (the body of) your Question. Possibly you chose the tag elementary-set-theory in connection with this, but it doesn't fit the tag wiki.
The post ends with "How is this still counted as a reduct?" (the only query evident in the post). But reduct is not defined for your Readers (nor is the term core appearing in the title and in the graphic, but not otherwise mentioned).
In this (now on Meta Math.SE) post you mention Computational Intelligence, which sounds like a mathematically based discipline, but not one I'm familar with. Possibly you would benefit from searching for related posts on CrossValidated SE, which treats not only statistical problems but also machine learning. Searching there for "rough sets" located one unanswered Question and four upvoted Answers (to other Questions).
Reasoned mathematical arguments about whether or not something is a reduct must rely on a formal definition of that, not merely on an example. I take it this is motivated by a project you are interested in, so perhaps you will be able to supply (if only by linking to a tutorial or the original Powerpoint presentation) Readers with such definitions.
Let me respond to the most recent Comment by OP above:
So you mean that I need to explain each term in the question? I myself don't understand enough to confidently define it, that is why I asked a question. I mean, I thought the intelligent people here could clear that up, but apparently I need to explain something I don't even understand? How does that work?
It is not necessary to explain each term in the Question, but you have asked about a problem on Math.SE. Reasoned mathematical arguments must proceed from formally defined notions. You might, as I already suggested, have linked to the source of the Powerpoint presentation you are asking about (it might provide the essential definitions) or to other papers, etc. where these essential terms are being used.
More important is the expectation that "the intelligent people here" should fill in the definitions because you "don't understand enough to confidently define it." It cases of this kind my recommendation is to drop back and ask a more threshold Question. We need you to ask a problem that you do already understand well enough to recognize as correct, thus avoiding the issue of blindly accepting what "intelligent people" say must be right. Mathematics is all about people understanding things for themselves at the end of the day.
What would be a good threshold Question here? Presumably you are studying classifiers in machine learning, and perhaps you've come across a Powerpoint presentation on the "rough sets" approach. If you want links to tutorials or survey papers that will fill in the blanks of that presentation, you would do well to identify it (proper citation with author(s) and provenance) and explain a bit about what essential terms need a better definition than "by example."
