Thanks for the input people, you have cleared up a lot!
The notion of cosets is quite confusing, at least to me. They've made their appearance in a chapter on Vector Spaces and I haven't seen them before.
Another minor detail I have come across is this (perhaps my set theory is lacking!):
if 2 cosets are equal, u + W = v + W, where u & v [itex]\in[/itex] U, then u - v [itex]\in[/itex] U [itex]\bigcap[/itex] W.
How is this the case? Is it simply set theory?