For each of following sets decide whether it is open, closed, compact or bounded:
(a) $\left\{ (x,y)\in\mathbb{R}^2 : \sin\left( \sin\left( \cos(xy)\right)\right)=\sin\left(\sin(x+y) \right)\cdot y , \ x\ge -1 , \ y\le x \right\}$
(b) $\left\{ (x,y)\in\mathbb{R}^2 : e^{x+y^2}=\ln \frac{1}{1+x^2+y^2} \right\}$
The above formulas are so complicated that I guess there is some smart way to test everything without solving equations. Can anybody help?