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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:

1. Y
2. N
3. Y − X
4. X

Correct answer: Y

Solution

The set Y consists of all numbers of the form 9(n - 1), which generates multiples of 9 starting from 0. The elements of set X do not produce any multiples of 9 for natural numbers n, meaning all elements of X are already included in Y, making Y the union of both sets.

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