Question

Let $A$ and $B$ be two sets then prove that $A-B=B^{\prime }-A^{\prime }$. Where $A^{\prime }$ is the complementary of the set $A$.

Answer 1

Let $U$ be the universal set.

Then

$B^{\prime }-A^{\prime }$

$=(U-B)-(U-A)$ [ Using the definition of complement of a set ]

$=A-B$.

So $A-B=B^{\prime }-A^{\prime }$.