If X=4n−3n−1:n∈N and Y={9(n−1):n∈N} where N is the set of natural numbers, then X∪Y is equal to

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

A
X
B
Y
C
N
D
Y-X

Solution:

Clearly $X = {0, 9, 54, 243, \dots} and Y = {0, 9, 18, 27, \dots} \Rightarrow X \cup Y = Y$

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