One of my friend sent me this question. I think it is a wrong question
Why?
When we define topology on $X$, we talk about set of all subsets of $X$. Here $(1,2018]$ is not even a subset of $X$, so we can not say anything about whether it is open or closed in $X$.
$1$ and $2$ are indeed meaningless because $(1,2018]$ is not even a subset of $X$.
$3$ is not true because $1$ is not an interior point of it.
$4$ is also meaningless: $0 \notin X$ so it is not even a candidate to be a limit point of any subset of $X$. Its negation is really voidly true:
$0$ is a limit point of $A$ iff for all open sets of $X$, if $0 \in O$ then $O \cap A\setminus\{x\} \neq \emptyset$. But we never have $0 \in O$ so the implication is always true and so the statement on the right hand side is true and $0$ is a limit point of $A$ (whatever $A$ is). So we could defend the negation of 4 to be true, so likewise that 4 is false.