Show that the following sets are not connected:

(a) A := $\displaystyle {(x,y) \in R^2 : x^2 + y^2 \neq 1}$;

(b) B := $\displaystyle {(x,y) \in R^2 : xy = 1}$.

For this problem, do I just need to show that A $\displaystyle \cap$ B is the empty set?

If so, I would need to prove that for any x,y $\displaystyle \in$ A cannot equal any x,y $\displaystyle \in$ B, right?