Question

If $A=\{1,2,3,4,5,6,7,8\},B=\{1,3,5,6,7,8,9\}$ then $n\left(\right(A\Delta B)\times (B\Delta A\left)\right)$ is equal to

• A. $16$
• B. $18$
• C. $9$
• D. $12$

Answer 1

The correct option is C $9$

$A=\{1,2,3,4,5,6,7,8\},B=\{1,3,5,6,7,8,9\}$
$\Rightarrow A-B=\{2,4\},B-A=\left\{9\right\}$
$\Rightarrow A\Delta B=B\Delta A=(A–B)\cup (B–A)=\{2,4,9\}$
$\therefore n\left(\right(A\Delta B)\times (B\Delta A\left)\right)=3^2=9$