I need to prove that A is a subset of B if and only if A - B = the empty set.
I'm a little lost at how to do this... could someone point me in the right direction?
Suppose not. Suppose that A is a subset of B and A - B =! the empty set.
That is, WLOG, that A - B = $\displaystyle {x_i}$, some element in A.
Then A = B + $\displaystyle {x_i}$, but this contradicts the definition of a subset.
(I think this is sufficient, not entirely sure, but I think it follows intuition nicely)