Show that the following sets are not connected:
(a) A := ;
(b) B := .
For this problem, do I just need to show that A B is the empty set?
If so, I would need to prove that for any x,y A cannot equal any x,y B, right?
A set X is disconnected if there exist two open sets, U and V such that:
For (a), take and . It's obvious that . It is also clear that (simply because and vice-versa).
For (b), take and . Then proceed to show that: