Which one of the following is an example of nonempty set?

Options

A. Set of all even prime numbers
B. `{x:x^(2)-2=0 and x` is rational}
C. {x: x is a natural number, `x lt 8` and simultaneously `x gt 12`)
D. {X: is a point common to any two parallel lines}

Answer

To determine which of the given options is an example of a non-empty set, we need to analyze each option carefully. A non-empty set is defined as a set that contains at least one element. Let's go through the options step by step.

### Step-by-Step Solution:

1. **Evaluate the first option: Set of all even prime numbers.**
- The only even prime number is 2.
- Therefore, this set contains one element: {2}.
- Since it contains an element, this is a non-empty set.

2. **Evaluate the second option: x is a rational number such that x² - 2 = 0.**
- To solve for x, we rearrange the equation: x² = 2.
- Taking the square root gives us x = ±√2.
- However, √2 is not a rational number; it is an irrational number.
- Therefore, there are no rational numbers that satisfy this equation, making this set empty.

3. **Evaluate the third option: x is a natural number, x < 8 and x > 12.**
- The condition x < 8 gives us the natural numbers {1, 2, 3, 4, 5, 6, 7}.
- The condition x > 12 gives us the natural numbers {13, 14, 15, ...}.
- There are no natural numbers that can satisfy both conditions simultaneously, resulting in an empty set.

4. **Evaluate the fourth option: x is a point common to any two parallel lines.**
- By definition, parallel lines do not intersect; hence, there cannot be a common point.
- This means there are no elements in this set, making it empty.

### Conclusion:
Based on the evaluations:
- The first option (Set of all even prime numbers) is a non-empty set.
- The second, third, and fourth options are empty sets.

Thus, the answer is that the first option is an example of a non-empty set.