Find with respect to U=R in the following case.
The answer is How do you know if it's an open interval or a closed interval?
Since open sets do not contain their boundary, their compliment must contain all points that are in the boundary of the original set (where open) and not contain the boundary when it's there (when closed).
Think of the interval as a set of points. Note that -2 is in A and 1 is not in A. This means must contain -2, but can't contain 1.
Your answer is not correct. The answer is . -2 can't be in because it's in . 1 must be in because it isn't in . Is that clear? The compliment is just the set of points that aren't in its base.
Another way of saying that: the real line has no greatest or least element. It cannot be both closed and unbounded at the same time in the same direction, so "infinity" will never appear as the closed endpoint of an interval on the real numbers.