First slide

Operations on Sets

Question

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

Easy

A

N
B

Y-X
C

X
D

Y

Solution

We have,
$\begin{array}{l} \Rightarrow X = \{4^{n} - 3 n - 1 : n \in N\} \\ and X = {0, 9, 54, 243, \dots} \\ \Rightarrow Y = {9 (n - 1) : n \in N} \\ \Rightarrow Y = {0, 9, 18, 27, \dots} [put n = 1, 2, 3, . . .] \end{array} [put n = 1, 2, 3, \dots]$
it is clear that $X \subset Y$
$∴ X \cup Y = Y$

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