The given set \( G = \{x \mid x \in \mathbb{Z} \text{ and } x \leq 6 \} \) describes a set of integers (denoted by \( \mathbb{Z} \)) that are less than or equal to 6. 

Therefore, the set \( G \) includes all integers that are less than or equal to 6. The elements of the set can be written as:

\[
G = \{\dots, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6\}
\]

This is an infinite set of integers starting from negative infinity and going up to 6.

Would you like further details, or do you have any questions about this?

Here are five related questions to expand on this topic:
1. What is the cardinality of a set containing integers less than or equal to a given value?
2. How do you describe the set of integers greater than a certain number?
3. Can you represent a similar set with rational numbers \( \mathbb{Q} \) instead of integers?
4. What is the intersection of two sets like \( G = \{x \mid x \leq 6\} \) and \( H = \{x \mid x \geq -2\} \)?
5. How does set notation change for representing inequalities with strict bounds, such as \( x < 6 \)?

**Tip:** In set notation, make sure to clearly specify the domain (e.g

Explore the set of integers less than or equal to 6 in set notation. This problem involves understanding inequalities, integers, and set theory concepts. Learn how to express and describe sets of numbers using proper mathematical notation. Suitable for students in Grades 6-8.

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