Multiple choice question from general topology Let $X =\mathbb{N}\times \mathbb{Q}$ with the subspace topology of $\mathbb{R}^2$ and $P = \{(n,  \frac{1}{n}):  n\in \mathbb{N}\}$ .
Then in the space $X$
Pick out the true statements
1 $P$ is closed but not open
2 $P$ is open but not closed
3 $P$ is both open and closed
4 $P$ is neither open nor closed
what can we say about boundary of $P$ in $X$?
I always struggle to figure out subspace topology. Though i am aware of basic definition and theory of subspace topology. I need a bit explanation here about how to find out subspace topology of $P$? 
Thanks for care

P is closed but not open because epsillion ball around p=(n, 1/n) in P Then there will be rational q s.t (n, p) is inside the ball hence p is not open 
