# Evaluate this statement / find the set

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

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?

• You are wrong: $1,2$, and $3$ are all elements of the interval $(0,4)$, so $X=\{1,2,3\}$. – Brian M. Scott Oct 16 '15 at 23:12
• Yes, I was undecided about these 2 answers...:) – Always learning Oct 16 '15 at 23:13
• 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 – Always learning Oct 16 '15 at 23:16
• @Mario: You can write it either way--they are the same set--but it is probably more convenient to write it as $\{1,2,3\}$. – Cameron Buie Oct 16 '15 at 23:17
• @CameronBuie Happily, the intersection is the same in all three ;/ – BrianO Oct 16 '15 at 23:34