Discrete Math - Union and Intersect of two sets EXAMPLE (Request)

EXAMPLE (request)
We have two sets X, and Y.
1) Find union (XUY) of these sets, and express in Set Builder Notation
2) Find intersect of X and Y, and express in Roster Notation
3) Find a set Z that is a subset of X and empty set = Z intersect Y

[VGx]

You are awesome!! Thank you so much for helping me with all of these problems. I'll be sure to share your channel every chance I get :)

[chekitatheanimatedskeptic]

I have a confusion between the notations. When I consider all the elements in a roster my conclusion looks right, but when I consider the interval it looks incorrect.

The problem asks to show the intersection between (0, 2) and Z.
I mean, as the first set dont actually have 0 or 2 the only thing that appears in both is 1, so my conclusion was {1}.

But the problem is, if I write the complement of said set {1} in R, it would be:
R - {1}

And in interval notation it gets very confusing to say:
R-{1} = (-infinity, 1) U (1, +infinity)

Is that correct or incorrect? I cant really tell.

Edit: (0, 2) there are considered in R, not in Z also wanted to mention that.