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We are given two sets:

- \( A = \{1, 2, 3, \dots, 13\} \)
- \( B = \{1, 2, 3, \dots, 24\} \)

The tasks are:

1. **The number of elements in \( A \):**

   Set \( A \) starts from 1 and goes up to 13, so the total number of elements in \( A \) is:
   \[
   |A| = 13
   \]

2. **The number of elements in \( B \):**

   Set \( B \) starts from 1 and goes up to 24, so the total number of elements in \( B \) is:
   \[
   |B| = 24
   \]

3. **The number of elements in \( A \times B \):**

   The Cartesian product \( A \times B \) contains all ordered pairs \( (a, b) \), where \( a \in A \) and \( b \in B \). The number of elements in the Cartesian product is the product of the number of elements in \( A \) and \( B \):
   \[
   |A \times B| = |A| \times |B| = 13 \times 24 = 312
   \]

### Summary:
- The number of elements in \( A \) is \( 13 \).
- The number of elements in \( B \) is \( 24 \).
- The number of elements in \( A \times B \) is \( 312 \).

Would you like further explanation on any part of this? 

Here are some related questions to consider:
1. What is the Cartesian product in set theory?
2. How do you calculate the number of elements in the union of two sets?
3. What would \( A \cup B \) look like for the given sets?
4. How does set intersection work, and what is \( A \cap B \)?
5. What is the difference between Cartesian product and a power set?

**Tip:** When working with sets, always check if they have overlapping elements, as this is important for operations like unions or intersections.

Let A = {1, 2, 3, ..., 13} and B = {1, 2, 3, ..., 24}. Find the number of elements in A, B, and A × B.

This problem explores the calculation of the number of elements in two sets A = {1, 2, ..., 13} and B = {1, 2, ..., 24}. It demonstrates the use of set theory concepts and the Cartesian product formula to find the total number of elements in A × B.

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