Question

If $X=\left\{4^n-3n-1:nbelongstoN\right\}$ and $Y=\left\{9(n-1):nbelongstoN\right\}$, where $N$ is the set of natural numbers, then $X\cup Y$ is equal to:

• A. $N$
• B. $Y-X$
• C. $X$
• D. $Y$

Answer 1

The correct option is D

$Y$

Explanation for the correct option.

Given : $X=\left\{4^n-3n-1:nbelongstoN\right\}$ and $Y=\left\{9(n-1):nbelongstoN\right\}$

For $n=1,2,3.....$

$X=\left\{0,9,54,.......\right\}$

For $n=1,2,3.....$

$Y=\left\{0,9,18,.......\right\}$

Therefore, $X\subset Y$. So, $X\cup Y=Y$.

Hence, option D is correct.