x(8 - x) > 0 and x ∈ N gives :

1. 0 ≤ x < 8

2. 1 < x ≤ 8

3. 0 < x < 8

4. 0 ≤ x ≤ 8

For x(8 - x) > 0

Either,

⇒ x > 0 and (8 - x) > 0

⇒ x > 0 and x < 8 ………..(1)

or,

⇒ x < 0 and (8 - x) < 0

⇒ x < 0 and x > 8 ………….(2)

But both conditions of equation (2) are not possible simultaneously.

From equation (1),

Solution set = {0 < x < 8}.

Hence, Option 3 is the correct option.