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I'm sure I'm missing a small step somewhere, but I just don't know where. sorry, $X$ is a set. $A$ and $B$ are subsets of $X$

First assume $A=B$

Therefore: $X \setminus A = X-B$

Now assume $X setminus A=X-B$. I need to get $A=B$ from this assumption. I tried doing this:

Let $x\in(X-A)$; therefore $x$ is an element of $X$ but $x$ is NOT an element of $A$.

Let $y\in(X-B)$; therefore $y$ is an element of $X$ but $y$ is NOT an element of $B$.

Since $x=y$, conclude $A=B$.

Does this make sense?

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    First: don't mix capital letters and lowercase letters. $x$ and $X$ will usually be taken to denote different things. Second: what kind of objects are you considering? Are these elements in a group? Are these matrices? Are these polynomials? Are these sets? (If they are sets, why did you mark it as [abstract-algebra] and not as [elementary-set-theory])? What? Third: what does "$xE(X-A)$" mean?2012-01-13
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    I *think* you are talking about sets. In that case, "$x$ is an element of $A$" can be written in $\LaTeX$ like so: `$x\in A$`, which will produce $x\in A$.2012-01-13
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    Hang on, if they're sets, then this isn't even true, because A or B could have elements that aren't in X. But the wording of the question certainly makes them sound like sets. Original Poster, please clarify!2012-01-13

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