Question

If $Y = \{ 9 ( n - 1 ) : n \in N \}$ then $X \cup Y$ is equal to

• A. X
• B. Y
• C. N
• D. None of these

Answer 1

Answer: (B)

Y

Answer 2

Since, $4 ^ { n } - 3 n - 1 = ( 3 + 1 ) ^ { n } - 3 n - 1$

=

=

(

= $\therefore$ $4 ^ { n } - 3 n - 1$ is a multiple of 9 for $n \geq 2$.

For $n = 1$ $4 - 3 - 1 = 0$, For $n = 2$ $4 ^ { n } - 3 n - 1$= $16 - 6 - 1 = 9$

$\therefore$ $4 ^ { n } - 3 n - 1$ is a multiple of 9 for all $n \in N$

$\therefore$ X contains elements which are multiples of 9 and clearly Y contains all multiples of 9.

$\therefore$ $X \subseteq Y$ ,

$\therefore$ $X \cup Y = Y$ .