Back when I just started learning all this stuff, I used to confuse elements of a set and its subsets. For example, I'd be easily stumped when asked what the elements and subsets of {a} were. Also, it's good to know why the empty set is a subset of any set and the proof/s that there are 2^n elements in a power set.
Slightly off-topic here, but flipping through this[1] Abstract Algebra textbook(2009), I found it amusing that the author thanks NSA for support among others :D.
