Let x_n = {4ⁿ - 3n - 1: n ∈ N}

Now x₁ = 4¹ - 3 * 1 - 1 = 4 - 4 = 0

For n ≥ 2, we have

      x_n = 4ⁿ - 3n - 1

=> x_n = (3 + 1)ⁿ - 3n - 1

=> x_n = ⁿC₀ + ⁿC₁ * 3 + ⁿC₂ * 3² + ............+ ⁿC_n * 3ⁿ - 3n - 1

=> x_n = 1 + 3n + ⁿC₂ * 3² + ............+ ⁿC_n * 3ⁿ - 3n - 1

=> x_n = ⁿC₂ * 3² + ............+ ⁿC_n * 3ⁿ 

=> x_n = 3² ( ⁿC₂  + ............+ ⁿC_n * 3^n-2 )

=> x_n = 9( ⁿC₂  + ............+ ⁿC_n * 3^n-2 )

Thus, x_n is some positive integral multiple of 9 for n ≥ 2

Hence, A consists of all positive integral multiple of 9 of the form 

9( ⁿC₂  + ............+ ⁿC_n * 3^n-2 ) together with 0

Now B = {9(n - 1): n ∈ N}

This shows that B consists of all integral nultiple of 9 together with 0

In fact, we have

A = {0, 9, 54, 243, ......}

B = {0, 9, 18, 27, 36, 54, ......}

Thus x ⊂ Y