Question

If $A=\left\{\begin{array}{c}{5}^n-4n-1:n\in N\end{array}\right\}$ and $B=\left\{\begin{array}{c}16(n-1):n\in N\end{array}\right\}$, then

• A. $A=B$
• B. $A\cap B=\varphi$
• C. $A\subseteq B$
• D. $B\subseteq A$

Answer 1

The correct option is C $A\subseteq B$

$A=\{5^n-4n-1:n\in N\}$

$5^n=\{0,16,112,..........\}$, substitute the values on $n$

$B=\{0,16,32,\mathrm{48...........}\}$

Clearly all the elements of set $A$ are existing in set $B$

$\therefore A\subseteq B$