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?

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- Sep 23rd 2009, 08:07 PMabsvaluesubset 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? - Sep 23rd 2009, 08:22 PMMacstersUndead
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) - Sep 23rd 2009, 09:08 PMabsvalue
That makes sense. Thanks for your help!