# For any two sets A and B, prove that :

Question:

For any two sets $A$ and $B$, prove that : $A^{\prime}-B^{\prime}=B-A$

Solution:

$\mathrm{LHS}=A^{\prime}-B^{\prime}$

$=A^{\prime} \cap\left(B^{\prime}\right)^{\prime} \quad\left[\because C-D=C \cap D^{\prime}\right]$

$=A^{\prime} \cap B$

$=B \cap A^{\prime}$

$=B-A \quad\left[\because C \cap D^{\prime}=C-D\right]$

$\mathrm{RHS}=B-A$So, LHS = RHS