Closure and interior of topology

Question

1) $cl(\mathbb R) $

2) $int ([1, \infty) \cup $ {3})

3) $ \partial (-1,\infty ) \cap $ {-3} it’s a boundary

My solution: 1) it’s same $\mathbb R $ 2) $(1,\infty ) \cap $ {3} 3) {-1,-3} Correct or no ?

Answer 1

1. Correct: it is $\mathbb R$.
2. Correct, but why didn't you just write that the interior is $(-1,\infty)$?
3. Wrong. Since $\partial(-1,\infty)=\{-1\}$, $\bigl(\partial(-1,\infty)\bigr)\cap\{3\}=\emptyset$. Unless you meant $\partial\bigl((-1,\infty)\cap\{3\}\bigr)$, in which case the answer is $\{3\}$.

Answer 2

In case 2) why do you write that the interior is the intersection of interiors? This may lead you to false , if for example instead of $3$ were $-2$.