15. Bonus: Give a second, different definition of B using set-builder notation. B = {0, 2, 4, 6, 8}

To provide a second definition of the set \( B = \{0, 2, 4, 6, 8\} \) using set-builder notation, we can describe the elements of \( B \) in a different way. One approach is to describe \( B \) as the set of all non-negative even integers less than 10.

Here’s a different definition using set-builder notation:

\[
B = \{ x \in \mathbb{Z} \mid 0 \leq x < 10 \text{ and } x \text{ is even} \}.
\]

### Explanation:

- \( x \in \mathbb{Z} \) specifies that \( x \) is an integer.
- \( 0 \leq x < 10 \) restricts \( x \) to be between 0 and 9, inclusive.
- \( x \) is even ensures that \( x \) is an even number, which gives us the set \( \{0, 2, 4, 6, 8\} \).

Would you like more details or have any questions about this? 

Here are 5 related questions to expand on this topic:

1. What is the set-builder notation for the set of all odd integers less than 10?
2. How would you represent the set \( \{1, 3, 5, 7, 9\} \) using a rule for odd numbers in set-builder notation?
3. What are some other ways to describe the set of all non-negative integers less than 10?
4. How can set-builder notation be used to describe infinite sets?
5. What is the difference between describing a set using set-builder notation versus listing its elements?

**Tip:** When using set-builder notation, always ensure that the conditions clearly and uniquely define each element of the set.

Explore a different definition of the set B = {0, 2, 4, 6, 8} using set-builder notation. Learn how to describe B as the set of non-negative even integers less than 10 through mathematical notation and constraints. Suitable for high school students and beyond.

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