The problem asks us to identify which of the given sets represents a null set (empty set). A null set is a set that contains no elements.

1. Problem Description

The problem asks us to identify which of the given sets represents a null set (empty set). A null set is a set that contains no elements.

2. Solution Steps

* Option a: $\{0\}$ contains the element $0$, so it is not a null set.

* Option b: $\{\}$ is an empty set, since it contains no elements. It is a null set.

* Option c: $\{\emptyset\}$ contains the element $\emptyset$, which represents the empty set. Therefore, it is a set containing one element (the empty set), and is not itself the empty set. So, it's not a null set.

* Option d: $\{x | x \text{ is an even and prime integer}\}$ represents the set of integers that are both even and prime. The only even prime number is

2. Since 2 is both even and prime, this set contains the element

2. Therefore the set is $\{2\}$, which is not a null set.

* Option e: $\{\emptyset, 0\}$ contains two elements: the empty set $\emptyset$ and the number $0$. Therefore, it's not a null set.

3. Final Answer

The set that represents a null set is {}.

The correct answer is b.