Question

If X = {8ⁿ – 7n – 1 | n ∈ N} and Y = {49n – 49 | n ∈ N}. Then ______.

Options

• X ⊂ Y

• Y ⊂ X

• X = Y

• X ∩ Y = Φ

Answer 1

If X = {8ⁿ – 7n – 1 | n ∈ N} and Y = {49n – 49 | n ∈ N}. Then X ⊂ Y.

Explanation:

Given that, X = {8ⁿ – 7n – 1 | n ∈ N}

= {0, 49, 490, ...}

And Y = {49n – 49 | n ∈ N}

= {0, 49, 98, ...}

Here, it is clear that every element belonging to X is also present in Y.

∴ X ⊂ Y.