MHB  Prove |X| = |Y| When X\Y and Y\X are Equipotent Sets

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Prove that if X\Y and Y\X are equipotent sets then |X| = |Y|.

The problem is that I've no clue where to start...

(Futile) attempt: There is bijection $f: X\backslash Y \to Y\backslash X$. For every $r_1 \in X\backslash Y$ there exists $r_2$ s.t. $r_2 \in Y\backslash X$. That's $r_1 \in X$ and $r_2 \in Y$. So there's a bijection $f: X \to Y$. :confused:
 
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Note that $X=(X\setminus Y)\sqcup (X\cap Y)$ where $\sqcup$ denotes the union of disjoint sets, and similarly $Y=(Y\setminus X)\sqcup (X\cap Y)$.
 
Evgeny.Makarov said:
Note that $X=(X\setminus Y)\sqcup (X\cap Y)$ where $\sqcup$ denotes the union of disjoint sets, and similarly $Y=(Y\setminus X)\sqcup (X\cap Y)$.
I'm not really sure how to use that.
 
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