Show that A\B, B\A, and AnB are disjoint

Question

anonymous · Answer

Would this be valid to say?...

Suppose $$x  \in A\B$$
$$=> x \in A "and \not \in" B$$
$$=> x inB\A   "or" AnB$$
=>  A\B, B\A, and AnB are disjoint

anonymous · Answer

sorry second implies should be x IS NOT in B\A or AnB

unklerhaukus · Answer

x∈A∧x∉B   x∉A∧x∈B

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anonymous · Answer

so they are not disjoint?

unklerhaukus · Answer

they are disjoint

anonymous · Answer

is the proof i rote enough to say if they are disjoint or not?

unklerhaukus · Answer

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unklerhaukus · Answer

i think you need another some more lines

anonymous · Answer

I have found this online "Since it is in A ∩ B and A\B it is both in A ∩ B which means that it is in B and it is not in B because it is in A\B. It can't both in B and not in B, so we have a contradiction of the statement that A ∩ B and A\B have an element in common and thus they must be disjoint." - http://answers.yahoo.com/question/index?qid=20100323213818AAB9iI4 But i dont know how to put B\A into the statement

unklerhaukus · Answer

maybe one that says         B =  B\A   $\bigcup$    A$\cap$B

unklerhaukus · Answer

proof by contradiction is one method