The problem is asking for the union of two sets, $A$ and $B$, where:

• $A = \{ x \mid x \text{ is a prime number} \}$
• $B = \{ x \mid x \text{ is an integer} \}$

Step-by-step explanation:

1. Set A (Prime Numbers):
   The set $A$ contains all prime numbers, which are positive integers greater than 1 that have no positive divisors other than 1 and themselves. Example: $A = \{2, 3, 5, 7, 11, 13, \dots\}$.

2. Set B (Integers):
   The set $B$ contains all integers, including both positive and negative whole numbers as well as zero. Example: $B = \{ \dots, -3, -2, -1, 0, 1, 2, 3, \dots \}$.

3. Union of A and B:
   The union of two sets, $A \cup B$, includes all the elements that are in either set, or in both. So, every prime number (from set A) will be included, as well as all integers (from set B).

   Therefore, the union of $A$ and $B$ will be all integers, as every prime number is an integer, and integers already cover negative numbers, zero, and positive integers.

Conclusion:

• The correct answer is:
  $\{ x \mid x \text{ is an integer} \}$

Explanation of other options:

1. $\{ x \mid x \text{ is a prime number} \}$ — This represents only the set of prime numbers, not the union.
2. $\{ x \mid x \text{ is a whole number} \}$ — Whole numbers are typically non-negative integers (i.e., 0, 1, 2, 3, ...), which is a smaller subset of integers, so this is not correct.

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Would you like further clarification? Or do you have any additional questions? Here's a set of questions to explore the topic further:

1. What is the difference between a prime number and a composite number?
2. How does the intersection of sets $A$ and $B$ differ from their union?
3. What is the concept of set difference, and how does it apply to $A$ and $B$?
4. How can you use Venn diagrams to represent the union and intersection of sets?
5. Can a set be both a subset and a union of other sets simultaneously?

Tip: When finding the union of two sets, think of it as combining all unique elements from both sets. No element is repeated in the union!