Question

If $A=\left\{n^3+(n+1{)}^3+(n+2{)}^3;n\in N\right\}$ and $B=\left\{8n,n\in N\right\}$ then

• A. $A\subset B$
• B. $B\subset A$
• C. $A=B$
• D. None of these

Answer 1

The correct option is D

None of these

The explanation for the correct option:

Given, $A=\left\{n^3+(n+1{)}^3+(n+2{)}^3;n\in N\right\}$

$\begin{array}{rcl}{1}^3+2^3+3^3& =& 1+8+27\\ & =& 36\end{array}$

$\begin{array}{rcl}{2}^3+3^3+4^3& =& 8+27+64\\ & =& 99\end{array}$

$\begin{array}{rcl}{3}^3+4^3+5^3& =& 27+64+125\\ & =& 216\end{array}$

$\therefore A=\left\{36,99,216\dots .\right\}$

Also, $B=\left\{8n,n\in N\right\}$

$\therefore B=\left\{8,16,24,32,40,48,....\right\}$

$\Rightarrow A\not\subset B,B\not\subset A$

and $A\ne B$

Hence, option ‘D’ is the correct answer.