Calculate the number of elements in the product of sets M = {1, 2} and N = {3, 4, 5}.

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The product of two sets, also known as the Cartesian product \( M \times N \), consists of all ordered pairs \( (m, n) \), where \( m \) is an element of set \( M \) and \( n \) is an element of set \( N \).

Given:

- Set \( M = \{1, 2\} \)
- Set \( N = \{3, 4, 5\} \)

The number of elements in the Cartesian product \( M \times N \) is the product of the number of elements in set \( M \) and set \( N \). 

Set \( M \) has 2 elements and set \( N \) has 3 elements.

\[
\text{Number of elements in } M \times N = |M| \times |N| = 2 \times 3 = 6
\]

Thus, the Cartesian product \( M \times N \) has **6 elements**.

Would you like more details or have any further questions?

Here are five related questions:
1. What is the Cartesian product of two sets geometrically?
2. How do you list all the elements in \( M \times N \)?
3. What if set \( M \) or \( N \) were infinite? How would that change the result?
4. How do you extend this concept to more than two sets?
5. How does the Cartesian product relate to matrix multiplication?

**Tip:** The Cartesian product forms a grid-like structure, with every element of the first set paired with every element of the second.

Calculate the number of elements in the product of sets M = {1, 2} and N = {3, 4, 5}.

Learn how to calculate the number of elements in the Cartesian product of sets M = {1, 2} and N = {3, 4, 5}. This problem demonstrates fundamental set theory concepts and explains how to use the formula for Cartesian products. Suitable for students in Grades 6-8.

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