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If $A$ and $B$ are twosets satisfying $A-B=B-A$, then which one of the following is correct?
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Verified Answer
The correct answer is:
$A=B$
We drawthe Venn diagram,
$A-B=A-(A \cap B)$ and $B-A=B-(A \cap B)$
$\mathrm{A}-\mathrm{B}=\mathrm{B}-\mathrm{A}$
$\Rightarrow \quad A-(A \cap B)=B-(A \cap B)$
$\Rightarrow A=B$
$A-B=A-(A \cap B)$ and $B-A=B-(A \cap B)$
$\mathrm{A}-\mathrm{B}=\mathrm{B}-\mathrm{A}$
$\Rightarrow \quad A-(A \cap B)=B-(A \cap B)$
$\Rightarrow A=B$
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