Hey. This was a question I came across. What is the right answer?

If A and B are subsets of the Euclidean space,

and A + B ={x + y | x Є A and y Є B}. Then which of the following statements is false?

a) If A and B are bounded, then A + B is bounded

b) If A and B are closed, then A + B is closed

c) If A and B are open, then A + B is open

d) If A and B are connected, then A + B is connected.

I think options (a) and (b) are right. I am not so sure about openness and connectedness..