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Let X = {4ⁿ - 3n - 1: n ∈ N} and Y = {9(n - 1): n ∈ N}, where N denotes the set of natural numbers. Then X ∪ Y is:

1. X
2. Y
3. N
4. Y - X

Correct answer: Y

Solution

The set Y consists of multiples of 9, which are all natural numbers of the form 9(n - 1) for n in the natural numbers. The elements of set X, while defined, do not cover all natural numbers and thus do not include all elements of Y. Therefore, the union X ∪ Y is equal to Y.

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