Question

If $A$ and $B$ are two sets, then $\frac{A}{\left(\frac{A}{B}\right)}$ is equal to
$(\frac{A}{B}$ represents the difference of the sets $A$ and $B$ in this order.$)$

• A. $A$
• B. $B^{\prime }$
• C. $A\cap B$
• D. $A\cup B$

Answer 1

The correct option is C $A\cap B$

$\frac{A}{B}=A-B$
$\Rightarrow \frac{A}{B}=A-(A\cap B)$
$\therefore \frac{A}{\left(\frac{A}{B}\right)}=A-(A\cap \frac{A}{B})=A-(A\cap (A-A\cap B\left)\right)$
$=A-(A\cap A-A\cap A\cap B)=A-(A-A\cap B)=A\cap B$