Is {(1,1), (2,2), (3,3)} symmetric? transitive? Yes! Yes!
Why is R = {(1,2), (2,3), (1,3), (2,1)} not transitive? Because (1,1) and (2,2) are missing.
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So, is there a question here? Or are you just showing off?
Umm.. where does the "discrete" part of this question come into play?
Also, I wouldn't call the matrix symmetric. When I think of symmetric matrices, I think in terms of N x N (i.e. - square matrices.) The system you post is 3 x 2, three rows by two columns, which is not square.
Is {(1,1), (2,2), (3,3)} symmetric? transitive? Yes! Yes!
Obviously I'm not your grader, but I'd expect that you need to give some explanation along with your answers to get a full score. Other than that you are correct.
Why is R = {(1,2), (2,3), (1,3), (2,1)} not transitive? Because (1,1) and (2,2) are missing.
Again, the answer would be better if you explained why those would be needed for it to be transitive, but is otherwise correct.
So, is there a question here? Or are you just showing off?
The question's in the title (which admittedly is bad style): "Is this correct or not"
Also, I wouldn't call the matrix symmetric
It's not a matrix, it's a set of pairs that represents a relation.