If $A$ and $B$ are any two sets, show that $A^{'} - B^{'} = B - A$ .

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Solution

Let $U$ be the universal set.
We know that,
$A^{'} = U - A,$ $B^{'} = U - B$
$A^{'} - B^{'} = U - A - (U - B)$
$∴ A^{'} - B^{'} = B - A$

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