Can you help me subtract intervals? I was reading my abstract math textbook and they subtracted
$[3, 6] - [4, 8) = [3, 4)$. I was wondering if someone could write out how they got to $[3, 4$). I looked at wikipedia and it said I should go 
$[a, b] - [c, d] = [a-d, b-c]$. When I did this, I got $[-5, 2)$. I would be thankful for an explanation-- the book doesn't explain so it's probably really obvious-- but I don't know.

Let $I_1$ and $I_2$ be intervals in the real line. Then $I_1 - I_2 = I_1 - (I_1\cap I_2)$.
If $I_1 = [a,b]$ and $I_2 = [c,d]$ (note that $a < b$ and $c < d$) then there are some cases to consider:
If $d < a$ or $b < c$ then $I_1 - I_2 = I_1$ since $I_1\cap I_2 = \emptyset$.
If $a < c < b < d$ then $I_1 - I_2 = [a,c)$ since $I_1\cap I_2 = [c,b]$.
If $c < a < d < b$ then $I_1 - I_2 = (d,b]$ since $I_1\cap I_2 = [a,d]$.
If $a < c < d < b$ then $I_1 - I_2 = [a,c)\cup (d,b]$ since $I_1\cap I_2 = I_2$.
If $c < a < b < d$ then $I_1 - I_2 = \emptyset$ since $I_1\cap I_2 = I_1$.
