Answer:
An empty set, also known as a null set, is a set that contains no elements. In set builder notation, an empty set can be represented as follows:
1. x is an integer and x > 10, x < 5
- This set has no integers that satisfy both conditions.
2. x
- There are no prime numbers that are even.
3. x is a color of the rainbow and x is not a color
- No element can satisfy this condition.
4. x is a square root of a negative number
- The square root of a negative number is not a real number.
5. x
- No element can satisfy the condition of being both a country and not a country.
In each of these examples, the set builder notation describes a condition that no element can fulfill, resulting in an empty set.