The union of two sets $A$ and $B$, denoted by $A \cup B$, includes all elements from both sets without any repetition. The formula to calculate the number of elements in the union of two sets is:

$|A \cup B| = |A| + |B| - |A \cap B|$

Where:

• $|A|$ is the number of elements in set $A$,
• $|B|$ is the number of elements in set $B$,
• $|A \cap B|$ is the number of elements common to both sets.

Given:

• $|A| = 19$,
• $|B| = 6$,
• $|A \cap B| = 0$ (since there are no common elements).

Substituting the values into the formula:

$|A \cup B| = 19 + 6 - 0 = 25$

So, the number of elements in $A \cup B$ is 25.

Would you like further details or clarification on any part of this process?

Here are some related questions:

1. How do you find the intersection of two sets?
2. What is the difference between the union and intersection of sets?
3. How do you calculate the number of elements in the difference between two sets?
4. What is the role of the complement of a set in set theory?
5. How does the inclusion-exclusion principle apply to set union and intersection?

Tip: When calculating the union of two sets, remember that you only count each unique element once, even if it appears in both sets.