Question

If $A=\{1,2,3,4,5,6\}$, $B=\{1,2\}$, then $\frac{A}{\left(\frac{A}{B}\right)}$ is equal to

• A. $A,B$
• B. $B,$ $A\cup B$
• C. $A\cap B,B$
• D. $A\cup B$

Answer 1

Answer: (C)

$A\cap B,B$

Difference of two sets is given by $\frac{A}{B}$ or $A-B$. means all those elements of Set $A$ which is not present in set $B$.
$\therefore \frac{A}{B}=A-B=\{3,4,5,6\}$
Now, $\frac{A}{\left(\frac{A}{B}\right)}$ means all those elements of set $A$ which is not present in the set obtained above or in the set $A$.
$\therefore \frac{A}{\left(\frac{A}{B}\right)}=\{1,2\}$

$A\cap B=\{1,2\}$$\therefore A\cap B=\frac{A}{\left(\frac{A}{B}\right)}=\{1,2\}$.
Also, note that $A\cap B=\{1,2\}=B$.
Thus, correct answer for this question is $A\cap B,B$.