I am really confused about closed or open set,

I have options of choosing open, closed, or neither...

a) all x such that x<1 :I think it's open because tbere is some neighborhood of x0 which belongs entirely to S

b) All x such that x>= 0 : I think closed, because then 0 cannot have neighborhood?

c) all x such that either x<0 or x>=1 neither , because one side is open and the other is closed?

d)all rational numbers: neither?? because both rational irrational can be neighborhood

e)all irrational number: open

Are my answers right ??? and am I getting them right????