$X = (\{1\}\cup\{2,3\})\cap(0,4)$

I think the solution is an empty set but I would like confirmation or refutation from you.

I think it is an empty set because we take the union of 2 sets containing just those elements: $1,2,3$ and then we search for the intersection with the open interval $(0,4)$ - which means that 0 and 4 are not included. Thus, the 2 intervals share $1,2,3$ ... now, I feel even more confused but I keep thinking that the solution is an empty set. Am I wrong?

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    $\begingroup$ You are wrong: $1,2$, and $3$ are all elements of the interval $(0,4)$, so $X=\{1,2,3\}$. $\endgroup$ – Brian M. Scott Oct 16 '15 at 23:12
  • $\begingroup$ Yes, I was undecided about these 2 answers...:) $\endgroup$ – Always learning Oct 16 '15 at 23:13
  • $\begingroup$ What about if I would take only the union ({1}∪{2,3}). What would it be the result? = {1,2,3} or would the expression remain as is written? = {1}∪{2,3} ? Just for learning something I might need $\endgroup$ – Always learning Oct 16 '15 at 23:16
  • $\begingroup$ @Mario: You can write it either way--they are the same set--but it is probably more convenient to write it as $\{1,2,3\}$. $\endgroup$ – Cameron Buie Oct 16 '15 at 23:17
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    $\begingroup$ @CameronBuie Happily, the intersection is the same in all three ;/ $\endgroup$ – BrianO Oct 16 '15 at 23:34

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