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Can somebody please check my work!?

I'm just not sure about 2 things, and if they are wrong, all my work is wrong.

1. Find a counter example for "If S is closed, then cl (int S) = S

I chose S = {2}. Im not sure if S = {2} is an closed set? I think it is becasue S ={2} does not have an interior point, and 2 has to be a boundary point, (and 2 cannot be both and interior and a boundary point.) Im sure S={2} is closed!

cl (int S)

=cl (int 2)

=cl (empty)

= empty

and that is not equal to S = {2}

2. Let A be a nonempty open subset of R and let Q be the set of rationals. Prove that (A n Q) .... (I hope those symbols show, I got them from MS Word)

I figured that Since "A is a

**nonempty open subset**of R," A has to be composed of MORE than 1 element, hence, A has to have 2,3,4.... elements.

And I know (from lectures and the text book) that between any 2 real numbers, their is a rational. Hence, (A n Q) .

How does that sound? Can somebody please check this? Thanks in advance.