Correct Answer - Option 2 :
{x : 7 < x < 8, x is a natural number}
Concept:
The empty set is the unique set having no elements; its size or cardinality (count of elements in a set) is zero.
Calculation:
1. x: x + 4 = 7
⇒ x = 7 - 4 = 3
∴ {x: x + 4 = 7} = {2}
It is not a empty set.
2. {x : 7 < x < 8, x is a natural number} will be a null set because there is NO natural number between numbers 7 and 8.
3. x2 - x = 2
⇒ x(x - 1) = 2
⇒ x = 2 OR x = -1
∴ It is also not a empty set.
4. x2 - 3x + 2 = 0
⇒ x2 - 2x - x + 2 = 0
⇒ x(x - 2) - 1 (x - 2) = 0
⇒ (x- 2)(x - 1) = 0
⇒ x = 2 OR x = 1
∴ It is also not a empty set.
Hence, option (2) is correct.
