When an ice-cube melts in a glass of water, does the total volume increase or decrease?

Can someone settle a drunken dispute, with an explanation?
When an ice-cube floating in a glass of water melts, does:
a) the total volume taken up by combination of ice and water rise or fall, and
b) the water level rise or fall?

On the one hand, one would expect the ice to be more dense than the water, as it’s a solid, and raising its temperature would, one would think, cause it to expand. This would obviously suggest that the total volume will increase as it melts.

On the other hand, the ice floats, so it must be less dense than the water! This would obviously lead us to expect the volume to decrease, as the ice melts and becomes more dense.

(Assume no evaporation takes place.)

The part b question should be more simple, but I’ve included it just to check.