 Translate the tabular Form into Rule Form.

1. A = {2,4,6,8,10}

To translate the tabular form of set \( A \) into rule form, we need to describe the general pattern or rule that generates the elements of the set. The given set in tabular form is:

\[
A = \{2, 4, 6, 8, 10\}
\]

These numbers are all even numbers between 2 and 10. The rule form is a way of defining the set using a condition that all elements must satisfy.

### Rule Form:
\[
A = \{ x \ | \ x = 2n, \, n \in \mathbb{N}, \, 1 \leq n \leq 5 \}
\]

### Explanation:
- \( x = 2n \) means each element of the set is an even number.
- \( n \in \mathbb{N} \) specifies that \( n \) is a natural number (positive integers).
- \( 1 \leq n \leq 5 \) limits \( n \) so that we only get the elements \( 2, 4, 6, 8, 10 \).

Would you like more details, or do you have any questions?

Here are 5 related questions to expand your understanding:
1. How do we translate sets with odd numbers into rule form?
2. What if the set contained numbers with a different arithmetic progression?
3. How can rule form be extended to describe an infinite set?
4. How would you express a set of prime numbers between 1 and 10 in rule form?
5. How do we write the rule form of a set that contains non-integer elements?

**Tip**: When converting to rule form, look for patterns such as arithmetic sequences or specific conditions that all elements share.

Translate the tabular form into rule form: A = {2, 4, 6, 8, 10}

Discover how to translate the tabular set A = {2, 4, 6, 8, 10} into rule form using set builder notation. This problem explores arithmetic sequences, even numbers, and provides a detailed explanation for students in Grades 6-8.

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