What is the difference between using ⊂ and ⊆? My book was not particularly lucid on this topic.
Depends on the author. Usually, the two notations mean the same thing, that is: [itex]A\subset B[/itex] or [itex]A\subseteq B[/itex] means that all elements in A are also in B.
Other authors (but a minority!) use [itex]A\subset B[/itex] to mean that A is a subset of B but A is not equal to B.
You should check your book to see which convention he uses.
Separate names with a comma.