1. Consider the metric space X = (Q ∩ [0; 3]; dE):

(a) the the point 2 is an interior point of the subset A of X where

A = {x ∈ Q | 1 ≤ x ≤ 3}?

True. Since you can make an open ball around 2.

(b) The the point 2 is an interior point of the subset B of X where

B = {x ∈ Q | 2 ≤ x ≤ 3}?

False. Since you can't make an open ball around 2 that is contained in the set.

(c) The point 3 is an interior point of the subset C of X where

C = {x ∈ Q | 2 < x ≤ 3}?

True. Since you can construct a ball around 3, where all the points in the ball is in the metric space.

(d) Describe the possible forms that an open ball can take in X = (Q ∩ [0; 3]; dE).

I don't really get this question, but I think the possible forms are all balls in [0,3] . IS THAT RIGHT???

Is the other answers right.