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**Problem:**Let $B$ be a subset of $Y$, prove that $Y \setminus (Y\setminus B) = B$.

**Attempt:**Since we're given $B \subset Y$, I tried to show $Y \subset B$. Let $a \in Y \setminus (Y\setminus B)$. Then $a \not \in Y\setminus B. $ I'm unable to manipulate this to $a \in B$ -- because it seems perfectly possible for $a$ to be in neither $Y \setminus B$ nor $B$.