Thread: subset help

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 = , some element in A.

Then A = B + , but this contradicts the definition of a subset.

(I think this is sufficient, not entirely sure, but I think it follows intuition nicely)

That makes sense. Thanks for your help!