Possible number of dense subset of metric space $X$
I found the answer but i have some confusion in my mind
My attempt : If i take two non-isolated point that is $ p= \mathbb{Q}$ , $q=\mathbb{R}\setminus \mathbb{Q}$ where $p$ and $q$ are two non -isolated point , Then according henno Brandsma sir answer
Number of possible dense subset are
$1. c(q)$
$2.c(p)$
$3.c(p) \cap c(q)$
$4.\mathbb{R}= X$
But Here option 3 is not possible because $c(p) \cap c(q) = \emptyset= \mathbb{Q} \cap( \mathbb{R} \setminus \mathbb{Q}) = \emptyset $
we know that empty set is not dense.
Then How there are $4$ possible dense subset ?