define the set of all integers that are multiples of 5 using set builder notation

The set of all integers that are multiples of 5 can be defined in set-builder notation as:

\[
S = \{ x \in \mathbb{Z} \mid x = 5k, \, k \in \mathbb{Z} \}
\]

Where:
- \( x \in \mathbb{Z} \) means \( x \) is an integer.
- \( x = 5k \) means \( x \) is a multiple of 5.
- \( k \in \mathbb{Z} \) means \( k \) is any integer.

Would you like more details or have any questions?

Here are 5 related questions for further exploration:
1. How would the set of multiples of 3 be written in set-builder notation?
2. What is the intersection of the set of multiples of 5 and the set of multiples of 2?
3. How do we write the set of even integers in set-builder notation?
4. What is the union of the set of multiples of 5 and multiples of 7?
5. Can the set of multiples of 5 be a finite set? Why or why not?

**Tip:** Set-builder notation helps describe sets concisely by using conditions or rules to define membership.

Define the set of all integers that are multiples of 5 using set-builder notation.

Explore how to define the set of all integers that are multiples of 5 using set-builder notation. This explanation covers key concepts in set theory, including set-builder notation and properties of multiples. Suitable for high school students in Grades 9-12.

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