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Question

# $\Delta$ denotes the symmetric difference operator defined as $A\Delta B=(A\cup B)-(A\cap B)$, where A and B are sets. Is $\Delta$ commutative? If so, prove it; otherwise, give a counterexample.

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DEFINITIONS

$X$ is a $\textbf{subset}$ of $Y$ if every element of $X$ is also an element of $Y$.

Notation: $X\subseteq Y$

$\textbf{Symmetric difference }A\Delta B$: All elements in $A$ or in $B$, but not in both.

$\textbf{Commutative laws:}$ $A\cup B=B\cup A$ and $A\cap B=B\cap A$

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