Question

Let X = {1, 2, 3, 4, 5, 6}. If n represent any member of X, express the following as sets:
n ∈ X but 2n ∉ X

Answer 1

For X = {1, 2, 3, 4, 5, 6}

It is the given that n ∈ X, but 2n ∉ X.

Let, A = {x | x ∈ X and 2x ∉ X}

Now, 1 ∉ A as 2.1 = 2 ∈ X

2 ∉ A as 2.2 = 4 ∈ X

3 ∉ A as 2.3 = 6 ∈ X

But 4 ∈ A as 2.4 = 8 ∉ X

5 ∈ A as 2.5 = 10 ∉ X

6 ∈ A as 2.6 = 12 ∉ X

So, A = {4, 5, 6}